The M will have the better performance unless loaded up with a lot of extra weight to compensate for the built-in weight in the N. While the WEP is available, the difference is very small, but without it, you will see a much bigger difference in favor of the M. The weight affects mostly climb and level acceleration, while stall and slow handling is compensated in the N with the bigger wing.
The wing of the N was extended at the root to make room for the fuel tanks. As a result, the gun bays are even farther out than in the M. It means more convergence issues - i swear that if you shoot and LA7 from point-blank with a P47N, you'll only hit both wingtips of the La. The guns are that wide.
The M is just a late model D with a hot-rod engine. The hot-rod refers to the insane WEP power, but in MIL power it is just a D model. In practice, the 56th FG that got them already had their D's over boosted to the levels of the M, so the new plane was not a big improvement over what they already had. The N was intended for use in the PTO and it was all about extending the range of the P47 for escort duties - a job it lost to the P-51 in ETO due to range problems. It did not make the P47 any more economic by any stretch, it simply solved the problem by burning even more fuel per mission. If you want to enjoy a light P47, learn to manage fuel, RPM and throttle. You will transit slower, but have a longer quality time in the furball.