There was no mythical machine that won everthing for either side.
When you wrote that my first thought was of the P-51D Mustang. I always grew up learning this was the best fighter. Faster (true), more maneuverable, fast climbe, dive, etc. In fact, aside from some speed, is was in most respects just "very good". But it was "very good" in many many things. What made it so amazing was it's range, the training of it's pilots (US pilots got 50%+ more hours of training than Luftwaffe pilots by this time), and how changes in the conduct of escort operations at about the time this fighter was coming into large use.
In early '44 the escort operations were switched from going out with the bombers, covering them as they dropped bombs and then returning with them, to using three different sets of fighters, one for each phase of the bombers mission. This increased the available fuel each fighter had for combat emergency power from 5 minutes on a mission. They also changed engagement priorities. At first the fighters were to stay with the bombers. They could chase off enemy fighters but ended up not getting to engage them. Since later they had more combat time and more fighters, they were given instructions to give chase since downing enemy fighters was part of the destroy-the-luftwaffe endgame.