Two different species - Cultivation and harvest:

Flax (linen) is Linum usitatisissimum is a member of the genus Linum in the family Linaceae. It is a food and fiber crop that is grown in cooler regions of the world. In addition to referring to the plant itself, the word "flax" may refer to the unspun fibers of the flax plant. The plant species is known only as a cultivated plant. NOTE: Flax becomes linen when it is spun into thread.

Hemp is a commonly used term for high-growing varieties of the Cannabis plant and its products, which include fiber, oil, and seed. Hemp is processed into products such as hemp seed foods, hemp oil, wax, resin, rope, yarn and cloth, pulp, paper, and fuel.

Flax grows well in many climates, but does grow best in Northern Europe near the North and Baltic Seas. It needs a good weeding when about 4 inches high and some wind protection to prevent lodging. Moisture requirement high. Harvesting is done by pulling the plants out by the roots, drying and retting the stalks, breaking, and hackling.
Flax is incompatible with itself needing 5-7 years between crops on the same field.

Hemp grows rapidly with little intervention until harvest. Hemp grows so vigorously that weeds are not a problem. It is pulled up by the roots and either dried, retted, broken and hackled much the same as linen, or pulled up and chemically processed
Hemp is self compatible and improves soil for rotation by suppressing weeds. Hemp yields more fiber per acre with less work.

Yarn Production:
Both plants produce a stem fiber that is quite long and very durable. Properly processed hemp and linen yarns produce durable and long lasting fabrics.
Both fibers are hackled and spun with similar methods. The longer fibers are usually wetspun to make them smooth. The shorter fibers (tow) are also spun - wetspun for the finer fibers and dryspun for the rougher fibers. Dryspun bast yarn is typically hairy in comparison with the wetspun "line" fibers.
The two fibers are so similar that there is a range of properties that is interchangeable. Hemp is usually coarser than flax. Hemp is rougher. Good quality tow linen is comparable to quality line hemp.
The spinning process, amount of twist and yarn finishing are the same for both fibers. Exact spinning technique depends on intended end use.

Fiber Properties

Flax (linen) is smooth, has sheen, and produces a smooth strong yarn. The fabrics made from linen yarn are elegant, have a smooth crisp feel, and the sheen allows production of damask fabrics - tone on tone in white/natural.
Linen is superior for elegant clothing and household textiles. Linen requires considerable care when laundering to retain its elegance and beauty

Hemp is strong, slightly rougher than linen, is not as crisp - has a "buttery" feel when woven. Hemp is more mildew resistant making it suitable for technical fabrics, sackcloth, maritime fabrics (sailcloth), ropes and cordage. Hempen fabrics do not require as much care when laundering.

Woven Fabric Properties

Linen has a smooth, elegant feel. Linen fabrics are generally woven finer. Linen has a crisp feel. Linen underscores the beauty of high end fashion apparel and table linens. No other fiber can match the beauty of pure linen damask. Undyed linen tends to bright white

Hemp is "rustic" in its appearance and appeal. The coloration when bleached is always a little on the creamy side. Hemp yarn tends more to hairiness. Hemp fabric is often coarser than linen - typical examples are canvas, sacking, twill jeans fabric,

What to use?
Since both hemp and linen have excellent properties for making lovely handwoven fabrics, the desired finished goods will determine which of the two fibers is chosen. If rustic farmhouse towels or a simple work shirt are the goal, more than likely using hemp will contribute to a pleasing end effect.
On the other hand, when the desired textile is a damask tablecloth, white on white - there is no substitute for using linen.
As far as sustainability issues play a role, both fibers leave a footprint. The best way to make good use of one of these fibers is to create something that will be used and loved for a very long time. By using fiber in moderation for durable and lasting fabrics, we lower the need to plant and process more fiber.

TYPES OF LINEN FABRICS

Pure Linen
Beautiful, traditional fabric.
Tends to be quite stiff when new but becomes more flexible with repeated washing.
Quite expensive.
Often deemed difficult to weave or care for.
Linen wrinkles, but "nobly". A linen blazer will look more fashionable when worn than an imitation made of other bast fibers, rayon, etc.

Half Linen
A traditional European fabric, produced ever since ca. 1830 when cotton warp yarns became readily available. Usually cotton warp with linen weft, but could be reversed with linen warp and cotton weft.
Softer than pure linen. Generally easier to weave with elastic cotton warp. Easier to launder and iron.
Good way to put lasting color in household fabrics because cottons don't fade as quickly.

Half Linen with Cottolin yarns
Recently developed yarn. Uses "cottonized" short fiber linen. Interesting yarn, but rather expensive. Colors not as permanent as price would indicate.
Fabrics from Cottolin yarns ARE lovely. Provides both color intensity and elasticity lacking in pure linen.

Pure Hemp
Similar to pure linen.
Slightly rougher feel.
Becomes "buttery" when used.
Wrinkles with firmer creases and less beauty than linen.

LINEN (or Hemp) YARNS

Linen and hemp yarns are produced today in excellent quantity, just not "specifically for handweavers" as might have been true in the past. There are mills in Europe producing nice yarns that weave up well and are durable. Countries of origin include France, Belgium, Netherlands, Sweden, Finland and the Baltics. In addition to the standard weights - there are many finer yarns produced that are not found in weaving shops. The makers of these yarns generally require such massive minimum order quantities that they are sold only to factories. Mostly these are small mills that do not have what many wish to have in terms of "branding". Often a particular mill makes only a limited range of yarn and ranges of dyed material can be seriously limited. Weavers wishing to work with linen and hemp need to be able to make use of what is available rather than dreaming of something that is not made.

Line linen:  While it is reported that flax fibers can reach 24" to 36" in length, commercial line flax is spun with fibers averaging around 15". This is in no way poor quality yarn.

Tow linen can be spun from fibers that are nearly as long as line flax or very short approaching cotton. Naturally, the longer and finer the fibers, the nicer the yarn. Tow linen is nothing to be snubbed - while perhaps not suited to white damask, household and clothing fabrics are lovely made of tow linen. Tow can have more "character" in the form of slubs and other imperfections.

Cottonized fiber (cottolin) is using short tow that would otherwise be scrap blended with short cotton. The resulting yarn is much like an unmercerized cotton  with a slightly deep shade after dying. It does not substantially make a difference in the hand of a fabric, but the natural version adds lovely color to cotton projects.

Yarn Construction

Singles

Plies

Traditional linen fabrics are woven with singles yarn in warp and weft. This is what guarantees the smoothness and sheen associated with linen. Damask requires light refraction that only comes from a smooth singles yarn - 2-ply absorbs the light instead.

Plied linen (hemp) yarn will put texture into a fabric, much the way that Oxford cloth gives the cotton a recognizable texture. Two ply yarn gives a nice fabric. More than 2 plies are best used as tapestry or rug warp as even in finer grists, they tend to be inflexible woven into fabric.

Yarn Numbering

Lea System (English measurements)

Metric System

1 lea = 300 yd   Yarn number is leas per pound.

Yarn number is 1000's of meters per kilogram

8/1 linen yarn = 8 * 300 or 2400 ypp

5/1 linen yarn would = 5000m/kg or 2500m/500g

16/1 linen yarn = 16 * 300 or 4800 ypp

10/1 linen yarn would = 10,000m/kg or 5000m/500g

Ypp (yards per pound) is, for all practical purposes the same number as the meters in 500g. By this example a 16/1 linen yarn would correspond to a 10/1 metric linen. The hemp yarn from Romania is labeled 10/1 and then the number of plies - so it is 16/1 either as a single or plied 2-, 3- or more ply. The Lithuanian linens on Etsy are metric yarn numbering. The Scandinavian linen yarns sold by weaving shops are usually Lea numbering. Any supplier dealing with textile mills is most likely using metric numbering.

Colors

Natural, Quarter bleach, Half bleach, Full bleach, Dyed

Dyed yarns are dyed with fiber reactive dyes and are quite fast. There may be dye molecules not yet rinsed out, washing in HOT water with Synthrapol or Dharma's substitute product is recommended.

Quarter bleach - is slightly bleached to give the yarn a light golden color. Lovely, but will not last with repeated washings - more for wall hangings and other decorative pieces.

Half bleach - is yarn bleached to appear white, but is still actually an off-white. This allows the yarn to retain strength during the weaving process. By bleaching to this point, it takes only a few washes until the project is blindingly white.

Full bleach - is bleached to a bright white on the cone. If this is for a decorative piece, it is useful. Otherwise, when purchasing linen for a project, half-bleach is what is needed for "white".

Woolgatherers does not carry full bleach or quarter bleach yarns at this time.

WEAVING WITH LINEN

Linen is reported to be difficult to work with, need special misting and humidifying, and need special treatment. Actually, linen is nothing more than a thread that forces a weaver to use best practices as recommended in most basic weaving books. Linen does not allow cheating or shortcuts - and often when the weaver tries these and experiences difficulty - the thread takes the blame.

Linen Loves Simple Structures
Nothing is more elegant than a simple fabric in plain weave linen. It also wrinkles easily and is difficult to iron smoothly.
Twills, lace weaves, M's & O's, huck, spot weaves make lovely linen fabric. In fact, using these structures will help make ironing them a little easier.
Linen gives stability to open, lacy fabrics such as curtains, transparencies and room dividers.

Linen behaves better with high humidity. Generations ago, linen weavers sat in damp basements to produce a finer product. Midwestern summer weather is perfect for keeping linens in line.
If the natural humidity isn't enough, Bobbins may be dampened (best if plastic or stainless bobbins are used) Warp may be misted with water (or add a little starch to protect the threads). If the linen behaves without adding moisture, consider it a nice advantage and work without water near the loom.
Also, after weaving, always iron when damp or with PLENTY of steam.

Warping method.
It is recommended that the warp be wound on the beam under tension prior to threading any heddles or sleying the reed to provide opportunity for even tension and no abrasion while winding on. Back to front or sectional work best.

Wind linen bobbins carefully. Whatever technique is used, care and precision are required to keep the stubborn thread from jumping off the bobbin onto the axle of the shuttle. Not a fatal flaw, but VERY annoying.

Linen doesn't shrink. When planning a project take this into account.
The piece will remain very nearly the same size it appeared on the loom. This means that sett should be carefully monitored as it will remain as seen on the loom. On cotton warps, sett the cotton closer than usual as the weft will not shrink as much as cotton would.

Warp Sizing
Failure to size linen warps may not result in breakage, but will expose the thread to abrasion in a way that will lead to "shopworn" fabric off the loom.
Simplest sizing method is to dip the choke tied warp chain in diluted laundry starch (StaFlo or Argo). Line dry and warp as usual.

Sett
As linen yarns are rather fine, this might be a good time to begin calculating set using centimeters rather than inches. First, wrap yarn as close together as possible without overlapping around a measured segment (1 cm. or 1 inch). For a good solid tabby, divide the wraps/unit by 2.Then add 1 or 2 threads for a cm. Or 2-4 for an inch for good measure. A solid twill structure results in taking this tabby figure and multiplying by 1.5 or a little bit more. For transparencies use about half the threads needed for tabby. For lace weaves, make the tabby a bit looser.
This is NOT an exact measurement, but will over time help an experienced weaver eyeball yarns

Linen does NOT retain dyestuffs as well as other fibers.
Fiber reactive dyes on the market (especially in European yarns) may lead to bleeding and fading. To set these dyes, the FIRST washing (or contact with water) must be with water HOTTER than any expected later laundry cycle. That is, if the object might be subjected to a HOT cycle, pour boiling water over the newly woven fabric. This will permanently set the dye up to the temperature used in this finishing step.  Synthrapol is also recommended to catch bleeding dyes.

Objects subject to frequent laundering might be designed to have color in cotton yarns and the linen left natural or bleached.

Abrasion Resistance
While linen is one of the strongest yarns available, it is NOT resistant to abrasion. This means that in the reed, a linen warp will produce a lot of lint and possibly wear through. It is advisable to size linen warps to prevent this. Simple laundry starch is an excellent sizing - and has been used for centuries.

Linen yarn is relatively inelastic.
This means that the warp must be wound on as evenly as possible. Use plenty of warp sticks or place newspaper between layers.
Be careful throwing the shuttle on a linen warp. Snags from hitting warp threads do NOT shrink back in, but remain loose throughout the rest of the warp.