Lol Half Moon:
-j.A has more range than full moon, it's kinda a karate chop looking thing. Don't know if it's better or worse than Crescent j.A.
-5A is shorter than Crescent, but longer than Full. 2A is same as Full, the ground poke thing, it hits low.
-5B is same as MBAC. It actually has range.
-5C is same as Full, except it's cancellable like Crescent. It's pretty nice, makes it more useful than MBAC 5C outside of combos.
-236 is different from both other styles. Instead of hopping, she does a dash. 236A is a short dash, 236B is a really long dash where she's ducking down sort of, 236C is a short dash, comes out about as fast as MBAC 236C. Her 236B looks better, since it's like as fast as her old 236B but she moves forward a lot and she doesn't get hit by high attacks. Don't know if that makes it usable though.
-623A/B/C are like MBAC. No 623A uppercut, no chargeable 623A or 623B. Probably some startup/active/recovery data was changed, but in the other two styles 623 was changed drastically, in Half it's basically the same thing.
-214A/B can't be charged. They're the same as MBAC, except you still can't jump cancel 214A on block.
-No aerial EX bite in this style. It's crescent only.
-No dunk. She shares the same number of specials as MBAC, while the other two styles got extra specials.
-22A/B is same as Full... kinda. 22A is slow while 22B is fast. I think for some characters the designers switched around commands between A/B for no good reason, like Full Kouma has the same 22A/B as MBAC I think, but for Crescent 22A is the teleport and 22B is the attack. Regardless, I think 22B is like Miyako's 22A, and same use for ending blockstrings. 22A is slower, IIRC doesn't knock down, I think it's meant to be a stagger than you can combo out of.
-She has a "rolldodge." When you do it she floats forward. Also I don't know if this is Half only or Crescent and Half but using a Dodge weakens your guard bar, though only half as much as whiffing a shield would.
-j.B and j.C act like everyone else's j.B/C. Her j.C is weaker so she does less damage in Half than with any other style, but it seems like a much better move. It doesn't groundslam in air to air, so it sort of replaces j.B CH fishing, and it's jump/dash cancellable on hit and block. Yes, this means Half Moon actually has real pressure. She can do j.C ad. j.C or j.C 2C mixups that everyone else can. And I think this applies to every style, but it feels like j.C's hitbox was adjusted to reach behind her. I was getting j.C crossups a lot more in MBAA than the extremely rare j.C crossups I got in MBAC.
So Half Moon might actually be the best style, despite it becoming just another typical character. Meh. I have fun with it. If you really want, you can do damage loops with 2C 3C 5C 623B into OTG 623C like you could in MBAC. Her bnb from videos is 2A 5B 2B 3B 214A j.BC j.BC j.throw, but I think there's ways to optimize it past that.