EDIT: The M and N have the exact same engine... Horsepower is identical. Only issues are frame-related or weight-related.
not quite Krusty but very close...while you are correct that both engines produced 2800 horsepower in war emergency, the R2800-57 only equipped the first 500 P-47N's built. The remainder were all equipped with either the R2800-73, -77 or -81. Yeah, it's picking nits but the engines although similar, had slight differences between them, mainly the ignition system.
REFERENCE: White, Graham. (2001). R-2800, Pratt & Whitney's Dependable Masterpiece. Society of Automotive Engineers Publishing, Warrendale, Pa. (pp. 279, 283, 408-413)