Load Factor = G. Turn Rate at 9G is the same irrespective of speed but Turn Radius increases with speed. Excess thrust helps but only in a level fight, normally you just stick you nose low to maintain energy.
The AoA to achieve the required G reduces as speed increases and conversely when slowing down you run out of Aoa to achieve the required load factor and so cannot maintain the turn rate. This means the low wing loader does better when slower. So if an F-15 fought a Spit, the 15 would opt for rate, the spit for radius and the higher rate would generally enable the 15 to get the nose on earlier but maybe at min range.