I was reading a book a few months ago by an Australian who flew in New Guinea and ended up attached to the RAF in North Africa.

He said of the P40 and the Bf109 (words to this effect):

The P40 was a plane of strengths and weaknesses. We learnt very quickly how to use the strengths against the slower and 'weakly armoured' Zero's. But the Bf109 was a faster aircraft which could dive as quicklly and climb faster, so in a 'dogfight', the only real advantage was a tighter turn, which is handy but won't always win out (as it didn't with the Zeros).

I'm inclined to agree with all of this (as if I would know any better anyway). But in answer to the original question, much as I would like for the P40 to have been fitted with a better engine, more suited to it's good turning & handling abilities, it was never considered as a 'serious fighter'. Just a stop gap, until they could produce the replacements.

They kept using them though.........