The WWII pilots I have spoken with weren't very concerned with maximum speed. They were much more concerned with armament, combat speed, combat acceleration, turning, and rolling.
Normally, when they saw the enemy, they had maybe 15 - 25 seconds or less before closure, maximum ... usually less. That assumes an enemy fighter coming toward you, not a tail chase. Combat speed is the speed you'd be at if you started accelerating at max power upon sighting the enemy. It was usually around 300 - 350 mph, no more. Of course, Biff15 is right ... if you have a plane capable of 450 mph at your altitude, you probably have better combat speed and acceleration than one capable of 410 mph at that altitude.
If your aircraft was a good turner, you'd use turn rate to get on someone's tail. If your aircraft was a good roller, you'd use rolling maneuvers to avoid letting someone get on YOUR tail. Turning was more important for offense, roll was more important for defense. Speed was relatively unimportant as long as you had enough to close and fight or get away from a fight, whichever was appropriate for you at the time. WWII was not a conflict where vertical maneuvering was all that important because WWII fighters aren't all that good at vertical climbs. They aren't much use for more than 3,000 - 4,000 feet going vertical, and that's if they had a good turn of speed to start with.
The vertical is a lot more important for jets, especially once jets approach or have 1 : 1 or better thrust to weight ratios. If your thrust to weight is 0.5 or less, you're in a turning fight, more than likely. If it is 0.7 and up, you're likely in a vertical fight ... assuming fuel doesn't cause you to break off and run for home or a tanker. Somewhere in the middle of that is a scissors fight that can go upward or downward, depending on thrust. Whoever runs out of energy first is in trouble. The last place you want to be "out of airspeed, altitude, and ideas," which means you are in the gunsight reticle of the opponent.
I'd bet that Biff15, being an F-15 pilot, was likely very seldom, if ever, out of altitude, airspeed, and ideas, all at the same time! If it has nothing else, the F-15 isn't usually out of power unless maybe if you are flying on one engine.