Junky, different planes require different flap settings for the best sustained turn, but there can be more to it in a fight.
Here's an example that happened to me recently: both f4u1as, just came out of a maneuver that I can't remember, but it ended up with him about my 4 or 5 o'clock low, about the same or maybe he had a little more smash, I tried to go into the f4u's best sustained by putting out 2 notches while he already had all of his out. I would have gotten around on him eventually, but the problem was he had enough position already to spend the rest of his speed on making use of all of his flaps, and he got a shot. What I should have done was dump some more flaps, maybe not all of them because he had to climb to me which bled his speed faster than I would have bled mine, then after I defeated his shot and he was spent I would gradually raise flaps back to 2 notches and then sit and wait.
So some key things to remember are the one with more energy entering the circle will win unless the other guy has enough position already to drag it to a stalemate, and you need to be wary of the other guy spending everything he's got at the right time for a shot.
Also, sometimes doing those yo-yos as Violator suggests can help, but if you're in same planes, same weight, all you're doing is adding drag.
If you get on the losing end of the circle there is a way to escape if you're not too far gone already. Keeping at the edge of the stall (or wherever is best for your plane), raise flaps one by one, then very slowly easy off the pressure. Your mindset should be making the other guy turn as much as possible while you build speed at the same time.