Some of the things in Street Fighter are somewhat random so you get different results from time to time, like an attack doing massive damage one round and then barely any the next. It isn't so drastic that you'll always be complaining, but it's there and the effects will cost and win you matches if you play long enough. I haven't paid attention to HD Remix enough to see if they toned this down, though.
As far as specific changes to characters, David Sirlin (a tournament Super Turbo player that designed this game) wrote articles for each character detailing changes made and the reasoning behind them. You can find that here :: http://www.sirlin.net/sf :: if you want to check up on that.