It varies per character, generally characters get more HP(except Carl), faster/extra dashes, stronger attacks etc. Some get extra special moves/DD's, alternate normals, some get a completely new moveset unlike their normal versions.
U. Haku basically has infinite Mugen iirc. I don't main him so I'm not sure.
U. Makoto has a totally new move set that imitates the moves of Dudley and Makoto from SF.