Well the way I see it:
Cyclone form: The Cyclone form makes a lot of use of sweeping, flowing movements, mostly evident by CJ's kicks.
Heat forms: Very street brawl-y style. It's more of a high-impact style and it's really obvious through the series
Luna: Wacky but moreover whipping style.
Trigger doesn't necessarily show much style since it's a gun mode but LT is rapid and tricky, HT is still high-impact, and CT seems like a mix between both.
Fang, obviously supposed to be the wild bezerker style
Xtreme just shares the way a lot of Ultimate forms fight but it seems knighty with the sword and shield combo.