If the Air Force comes up with some awesome new tactic that makes them better in battle, I can't imagine it wouldn't be shared with the Navy and Marines for their pilots. I'm assuming that pilots from all arms train as much as each other. And the Navy has thousands of pilots - not quite as many as the Air Force, but there aren't as few as you might think. (It's like 10K to 7K, or thereabouts).
When it comes to who would win in a fight, it's probably more about who has the most advanced equipment, to be honest. I read an article after the F22 came out talking about how EVERYONE (F15, F16, and F18 pilots) were tired of losing to an opponent that they never even saw - they would call it a success to even get a target lock on an F22.