Here's my thoughts/breakdowns on the VAkiha moons:
Before reading what is to follow, I believe all 3 moons of VAkiha are highly viable. Whichever one(s) you pick, you have all the tools to succeed! While all VAkihas benefit from having 2 very quick air dashes and a great equally as fast ground dash, you are also playing the character with the least amount of vitality in the game. Sloppy game play will get you killed fast, which turns a lot of players off from her. Though her life is low, she has the great neutral and powerful okizeme to make up for it, regardless of what moon you are picking.
Full- The strongest VAkiha. She gets highest damage off random confirms out of any VAkihas. She can burn 100 meter to get an untechable knockdown now off any air combo, thanks to the CC making her j.236C awesome. Her neutral is awesome thanks to puffballs and air pillars, both move exclusive to Full moon style. Her corner carry is decent, but she will sacrifice a good knockdown in order to do so in most cases. (forced to end combos with air throw instead of 623B/j.236C) Her pressure is simple yet effective as her 5a/2a yield large amounts of frame advantage and her overhead j.A make for a good mixup option. Also, TK puffball (j.236A/B) is extremely plus on block, and even counts as a jump for VAkiha. Final comment about F is that her pits are a bit different from C and H. You can set up to 3, one for A, B, and C respectively. You can manually ignite these pits via repeating the command, (i.e. 22A 22A will set a pit then ignite it) or you can cause the pits to ignite automatically by putting an opponent in hitstun/blockstun while standing on a pit. Successfully confirming into a pit is an easy way to tack on large sums of damage to your combos. Out of all the VAkihas, her defensive options are weakest.
Half- My personal favorite style for VAkiha. H-VAkiha gets corner carry to the corner, into momiji loop (623B loop) knockdown off of anything and everything. Her damage in the corner is just shy of F's, but midscreen she loses a bit of damage because of increased proration on 6AAA. Her rushdown is equal to if not better than F's thanks to lots of normals that move her forward. Her pressure revolves around scaring your opponent into standing still via stagger pressure, then locking them in place with frame advantage from pillars or pits. Half's pits throw a mat of fire on the ground like Crescents, but automatically ignite themselves. This helps her neutral game quite a bit as you can punish characters from staying on the ground and trying to establish their own space or anti-air you. This will force opponents into the air a lot of the time, and Half has many strong air-to-air options, despite having no air projectile like F/C. Defensively, Half moon has access to the godlike half moon shield bunker, which helps if your opponent does indeed catch you.
Crescent- recently risen from the dead. Crescent has a j.C that gives an untech knockdown on its own, but is not jump or air dash cancelable, so this is good and bad. Her corner carry costs 100 meter to do, as you must combo into 623C. But, successfully doing this will land you a momiji knockdown + pit oki/air dash mixup, so its definitely worth it. Even if you don't use the meter, she has access to strong midscreen okizeme in the form of ambiguous left/right mixup. Her neutral is awesome because of long reaching flame ribbons (j.236a/b). Her pressure is similar to H's, but she uses TK j.236A ribbon to reset pressure and punish backdashes, and even bait DPs. Her pits are manual ignite, and while your opponent stands in a pit, it will drain their meter/health and add it to VAkiha's. Knocking an opponent down and setting a pit on them makes for a scary situation for the opposition. Defensively, she has heat activation as she is C.
Hope this helps!