You need to play on one of the lesser console intensive stages, this is a result of console hardware being a subpar PC when it came out and even more shit now years later.
The best stage for this is Training Room as it has the least shit going on, it’s very hard to lag that stage, almost impossible in a real match.
Other stages with very few if any problems are Danger Room, Daily Bugel, Metro City
Most stages can be played with few problems some like Shield Helicarrier (imo the worst stage to play on in any game ever, I will always repick if possible) are problematic for lag or color issues (black on black with shit flying everywhere).
Realistically there isn’t anything Capcom can do to solve the issue, if they want colorful interesting stages with lots of things in the back and lots of stuff happening in the foreground they will probably run into issues with the low specs of the hardware. Luckily they added less system intensive stages which allow for serious play, that was the main reason for the nightime Asgard, Daily Bugle and Black and White demon village (as well as allowing them to reuse models and work).
Seriously though you should be able to play on both PS3 and 360 the differences are so minor that it isn’t relevant, people make way to much of a big deal out of it, if you care to learn more about the actual differences as opposed to the ones that don’t exist or are misunderstood go look up the tech comparisons done when vanilla got released.