Compared the the Lightning, the Mustang had three advantages: better roll rate, a speed advantage of 15-20 mph, and it was much cheaper to build.
Advantages of the Lightning were: higher climb rate, better pitch rate, better acceleration, better gun battery and a more stable shooting platform.
In horizontal turn rate and range the two were very similar with the Lightning having perhaps a very slim advantage in both.
The Mustang's rep. is largely the result of the fact that very large numbers of them entered combat at a time when the quality of opposing pilots was in serious decline.
Actually, the bomber crews generally preferred the Lightning as escort, because the chance of mis-identification was less. A Mustang that tried to chase a '109 thru a bomber formation was going to be shot at by the gunners. A Lightning could do that without being mistaken for another attacker.