Looking at racial features, half-elf Drow seem to have all the "best" features of full drow, with none of the downsides.
Past the "Drow Weapon Training" trait, is there any major benefit to playing a full Drow Elf over the Half-Elf Drow?
The full Drow Elf racial features are the Elf's base racial traits Keen Senses, Fey Ancestry, and Trance, plus the drow subrace traits Ability Score Increase (from base race and subrace), Superior Darkvision, Sunlight Sensitivity, Drow Magic, and Drow Weapon Training.
A Half-Elf Drow variant's racial features are the base racial traits Fey Ancestry, Ability Score Increase, and Darkvision, as well as the variant trait Drow Magic.
Best Answer
Superior Darkvision is the major advantage
The most significant mechanical advantage that a Drow has over a Half-Drow, and indeed most other races, is their 120-foot darkvision. Drow can see in the dark about twice as far as most other creatures with darkvision, which - in their natural environment of the lightless underdark - allows them to effectively notice danger and attack enemies at ranges where their opponents can't possibly see them and fight back. A Drow engaging enemies at the edge of their darkvision and with room to manoeuvre is very difficult to keep in sight for long enough to actually take an action against, since equivalently fast creatures would need to dash in order to get close enough to see it; the Drow needs only to lure or ambush their enemies in a large enough cavern or long enough tunnel (or, on the surface, outside, on a moonless or cloudy night).
Drow have the Sunlight Sensitivity trait to balance this out, but most Drow would probably try to avoid being in direct sunlight anyway - they'll be out and about at night, or simply remain underground.
The full Drow also has automatic perception proficiency, whereas the Half-Drow must give up their Skill Versatility trait in order to use Drow Magic, so Drow get a bonus skill proficiency over Half-Drow using this variant.