The title is self-explanatory. Discussion on differences between styles of ryougi. I'll list off some simple move differences/similarities:
C-Ryougi:
Decent range
6c crossover move
No ground overhead
22x weak on comboability
Has dash-attack 623x, which is good range, only useful in corner, uncomboable, but quite unsafe
Has 421 and 214 options for her overhead slash, which give crossup options
63214c mixup rush which is very good at forcing damage
Decent AA
F-Ryougi:
Exceptional range
5b and 5c miss crouchers from outside close range
Fast ground overhead with good comboability
Has all three types of parries
22x much easier to combo in and out of
Has a dash with an abnormally large uncancellable window in the beginning
No 63214
Strong AA with 5b and jumping normals
H-Ryougi:
Has C-Ryougi's range, but F-Ryougi's 5C for a little more range
Has a parry and the dash-attack 623x
Has F-Ryougi's 22x comboability
Has F-Ryougi's ground overhead
63214 jumping knife....use is kind of unknown?