I've read somewhere that the loadings and slowdowns are not as worse when the game is running on a Memory Stick as opposed to a UMD. Can anyone confirm? This might affect my purchase decision.

I'm also really interested in whether or not the PSN version runs better than the UMD version.  I played the shit out of the original on PSX and was unable to tolerate the slowdown in this remake. 
 
The game is apparently slated to hit iOS as well which I think might be a pretty fun way to experience the game.

I've never played the UMD version, I've always had a Go so I can't compare. It runs pretty well from my experience though, I never had any major issues.

Even running the game off a memory stick the slowdown remains.  Apparently it's just bad code within the game and not a matter of what platform you buy it off or run it on.  It's always going to happen until they mend it with an update or something.  So this means that when/if the game hits iOS that it will probably have the slowdown unless mentioned otherwise.
 
However, it only seems to be a big deal to those that played the game on PSX where there was no lag.  Great game, definitely worth experiencing if you can get past the slowdown.