Unlike some posters here, I know fighter pilots. And, I know of some of the training they go through to the extent they are able to share without violating security. They are more than capable of taking the fight to any adversary.
I also concur that any fight against a capable adversary on their turf will be a tough one. Just as if they were to fight us on our own turf, it would be a bloody one.
You mentioned WWII. The Japanese pilots were no slouches either. The problem they had was a lack of advancement in aircraft nor did they rotate their pilots out to ensure new ones were being trained by experienced ones.
In Korea, it was a known fact the USAF often fought against MiGs piloted by Russians.