I flew the Ki-61 in a number of FSO and snapshot events, it certainly doesn't get the credit it deserves in Aces High. It's sluggish at slower speed, faster it goes it becomes a gem of the orient, given it faces its historical setup I've seen it against F4u's, P-47s, F4Fs, P40s and P39s.
It cannot compete in the Late War Arena, however that doesn't mean its totally useless - it can dive at very high speeds and turn without a problem, armored and its gun package is extremely deadly. Thus being said I haven't seen a P-40F vs a Ki-61 however, I would put my money on the Ki-61.
I've flown a P-40F in FSO and its a completely a dog at 20-25k, no where to compete against a 109, this doesn't say much because the Ki-61 is in the same class - its totally useless going above 16-17k where its speed drops and a P-40F becomes a little faster.
Taken down below 15k I believe the Ki-61 holds the advantage, given its flown correctly and uses its acceleration and roll rate, it can
be a nifty little plane - one of the few furballers i've ever seen (kermit) used it quite well in the late war main arena.