HD Remix feels extremely tight, even with just a standard controller. With many of the special moves easier to execute (like Fei Long's Flying Kick), HD Remix performs well all-around and gamers will also be able to plug in arcade sticks if they prefer. There are a few occasional moments of slowdown during matches, though I imagine that might very well be intentional and in keeping with the original version. Intentional or not, HD Remix looks and runs nicely and won't interfere with your gameplay experience.
I played an ample number of online matches both on the PS3 and 360 and each version ran very well with little to no slowdown. This is, I'm sure, thanks in part to the consulting that the creator of the GGPO networking system did with the team at Backbone. Because it's a highly precise 2D fighter, slowdown in HD Remix could definitely hurt the online experience so gamers with a slow connection might prefer local matches, but I found nothing wrong with the online infrastructure during my time with the game. Having a stable online option definitely adds to HD Remix's appeal so hopefully people will have reliable connections to enjoy the expanded pool of competitors.