When someone does an Ultra, or a Super for that matter, the screen pauses for a while but it still reads your inputs. So while the screen is doing its dramatic pause, you can mash the hell out of your own Ultra so as soon as the pause finishes, yours will come out. It is a pretty good tactic for most people to counter someone else's Ultra with your own Ultra, because oftentimes whoever did their ultra *last* will win. Depending on how quickly it executes.

This is one reason why Rose's Ultra is so dangerous, for situations like this. Most ultras give you 'super armor' during their execution, but most Ultras also have 'armor breaking' properties to them.

Something to consider!
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So, the Update. I haven't bothered (and probably won't for a while) with the actual fighting of the tournament mode, but I've checked out the Replay features of both the PS3 and 360 version. As far as function, the 360's version is by far superior.
Here's what the 360 replay allows you to do:
-Slow down the action
-View each player's inputs
-View each other's Attack Data (hit damage, combo damage, that kind of stuff)
-Save Replays

PS3 version:
-You can make one of 3 votes twice a second, up to 99 times: 'Funny, Awesome or Beautiful'. The icons are just up on screen as the replay goes on, and you see what other people have voted.

It's kind of pointless, but also kind of fun. I really don't know why they split the features like that--both versions could have had all of those features. The 360's version is functionally better because you can save the replays to watch whenever you want, even when not online, and it would be easier if you wanted to learn some things from a particular replay when you can slow down and see the inputs as well. Also, when I tried it out for the first time yesterday, the PSN wouldn't even let me download the replays at all, while the other version was completely flawless. PSN seems to be working fine today though.

This has gotten me 'back' into Street Fighter, since I took a break because school was getting kind of rough :P See how long that lasts...