I don't actually.
Just wondering which branch usually 'wins' against the other branch....
Gotcha, just thought you were trolling up an intra-service schlong-measuring contest.
The reality is that there just is no difference between services when it comes to that sort of thing. Obviously there are differences in specific aircraft capabilities, but because pilot skill and opportunity plays such a large role in 1 v 1 aerial combat, those differences in capabilities can often be negated or offset. It is similar to predicting the winner of a football game based just on historical stats.
In addition, there just aren't much in the way of opportunities to have a "bar brawl" where blue service and white service pilots can just bash it out to see who is best. Training time, gas, and money is so limited that opportunities to fight dissimilar aircraft have to be used to support very specific training objectives and scenarios...and those scenarios are rarely unrestricted 1 v 1 fights to see who wins, unfortunately.
Most of the time, these aerial engagements are set up with specific formations, specific tactics, specific weapons and specific scenarios for both the "good guys" and the "bad guys", and are designed to test or practice those specific items. Many times those scenarios include artificial restrictions on the capabilities of the adversaries to mimic the specific capabilities of real-world adversary aircraft or require specific tactics to be flown that mimic real world adversary tactics. Those scenarios are also often training grounds for pilots upgrading to higher responsibilities (like becoming a multi-ship flight lead, or qualifying as a new wingman, or upgrading to instructor), and as such the "good guys" might not even execute their own tactics at a proficiency level that a front-line, experienced pilot would do in real life. Thus, the "winners" and "losers" of these engagements can't just be taken in a vacuum as a referendum on who is best or which aircraft is best (which often happens, especially with the press looking at fighters of different countries going through large force exercises).
I have had only two opportunities in my entire career to have an opportunity to fight 1 v 1, "full up vs full up", against a USN aircraft. Both times it was against F-14s out of NAS Oceana, in an event called the "East Coast Strike Fighter Shootout" back in the early 00s. I've written about that experience before here on JC; I won one fight and lost the other.
So, despite all of the intra-service chest thumping about who is best that often takes place, when you strip away the bravado and just look at the capabilities of the pilots in the real world, they're all really pretty much just as equal as comparing the average capabilities of fighter pilots of the same service. No difference.