I have both consoles and Dual modded sticks so that isn’t an issue. I’m leaning on the PS3 version since I have a portable monitor for it. I’m pretty sure that graphics are identical, but I am wondering if any version has any slight edge like better loading times or better online.
The PS3 version has sixteen exclusive characters, including Rule 63 Mega Man.
With Double E’s.
The PS3 version has a custom soundtrack option.
THERE, an actual answer 
The PSN players are fraudulent
There are also reports of the 360 version getting abnormally long loading times. As far as I can tell the PS3 version does not suffer from this.
Consider that an apology for the obligatory joke answer. 
[LIST]
[]360 has a “exit game” option in your pause menu due to XBLA requirements. PS3 does not.
[]360 has longer loading times, which is due to the way the 360 handles security on files. MikeZ said that he will fix this in a later patch by adding batch loading.
[]360’s messages are at the bottom of the screen, where there’s nothing to block. PS3 messages are in the upper right, which block P2 health and super meter.
[]PS3 has custom soundtracks.
[*]Unconfirmed: 360 seems to have the hitboxes glitch a lot less than the PS3.
[/LIST]
That all sounds about right, but I’m playing on the 360 and have seen the hitbox glitch quite a bit. It seems to go hand and hand with the loading issue you mentioned previously.
I don’t think there’s really a big disparity between the two versions though, aside from the obvious differences between PSN and LIVE. They seemed to do a really good job at making them identical.
Unlike another game thats getting parodied in this thread… <_<
>_> you sir have just crossed the line