I can't set the keys to something like this:
Player 1 stick: A
Player 2 heavy: A
But I can set them to this (the same key for the same thing, but not the same player):
Player 1:
Stick: A
Slide: S
...
Player 2:
Stick: A
Slide: S
...
Of course it's fun, but there is no consistency, because Gish doesn't allow the former.
I'm running the demo.
It also happens in the new 1.2, so I'll 'bump' this thread. 
And now I have the full version for a while, I tried it with dragster, resulting in different results for Gish and Gray. Is that float precision, random or something else?
Replays are not cross-plateform compatible. So your replays on OSX will not work on Windows.
Though I'd bump this again, since it hasn't been answered, and it has me curious myself. It's worth noting that for the first 10 seconds or so there is zero discrepancy between gish and grey, and then they become radically different. I've literally managed to have one player finish the race with the other not across the start line (after about 5 minutes of fiddling about
). Which explanation this supports... I dunno.