Well, the difference in wing shape does actually lead to several differences. Aside from the "now clear" gun position change, add center of gravity difference, fuel tanks in the N, flap difference, plus lift to drag ratio, amongst all other aerodynamics changes because of the size diff in the wings. One physical change leads to a bunch of differences to flight, adding weight and drag/lift differences and you might call it tens of differences.
I understand what you're trying to say, but unless we do the math, we don't know how drastic any of these "differences" are. I keep saying "from a
performance perspective" because that's a very important qualifier. I mean, if you really want to get detailed, the N had an autopilot, tail warning radar, rudder pedals that flipped down so the pilot could prop his legs up, a different turbo-charger, different power controls, etc. But the gun position (and landing gear as well--they moved out so that the aircraft had even wider mains) doesn't change how it performs conspicuously. You might say "well, with the guns and gear out further on the wing, it could affect roll rate". I'd say "perhaps, but how much impact do the larger ailerons with a longer moment counteract that?" We don't know unless we do some pretty scary math. What we can characterize is our perceptions in-game. I've flown the N a lot more than the M, but I don't notice a perceptible difference in anything other than climb, acceleration, and top speed (all due to the weight difference). Without looking it up, I'd guess the Cd of both aircraft are very close to each other. On a smaller, lighter plane, the changes that were made would have had a more conspicuous difference, but the P-47 is so damn big, the percentage differences get smaller.
If you get into the larger ailerons, larger flaps, lift-to-drag ratio and center-of-gravity issues, you need to do the math on them to make any sort of comparative statement. Obviously, my contention is suspect as well, because I haven't done the calcs either, but I suspect, especially for the CG, that not much changed from a performance perspective, other than the lower speed and climb due to the increased weight of the plane. You can argue that at very low weights, the N becomes more a better sustained turner due to lower wing-loading (bigger wing at equivalent weights), but again, I wouldn't say there's a conspicuous difference. For the most part, you can assume P-47N and P-47M performance to be equivalent, except for those flight characteristics affected by weight (climb and speed the most glaring).
Good discussion all the way around, and ditto Lepape--the effort to post that graphical comparison is very helpful.