In high-level Judo competition, the competitive gripfighting gurus say to always fight dominant side forward because it makes for a shorter entry for throws like seoinage. These gurus say that statistically (that is, looking at lots of past matches), folks that switch sides during a match never win.
But then, boxers always (or nearly always?) fight dominant side back, so that they can have greater power in their straight cross. I'm not a follower of boxing, so I don't know of any counterexamples or stats about boxers that fight on their off-sides.
So my question for y'all is, in a MMA-like environment, is it better to fight dominant side forward to facilitate grappling, or dominant side back to facilitate punching? Does it depend on the particular skills of the fighter? Does it matter?