D600 with D7100 as Back up

Duncan,

Let me see if I can get this straight, if I shoot with my D600 with the 80-200 at f2.8 at 80mm at 100 ft of the subject, then I shoot with the D7100 with the 80-200 at f2.8@ at 80mm at 150 ft, I will essentially get the same picture - same 24MP picture with more (elongated) depth of field, less distortion and less aberration with the D7100, right? I guess that is OK, the only difference would be that I have to back up 50 ft - if I have the room to do so.

If I do the same shot above, but instead of backing up I stay put. Might I get only 75% of the area (magnified 1.5 times) I shot before with the D600 - Same number of pixels, probably a better resolution of the scene so long as the cropped 25% is does not affect the actual composition. How about the Depth Of Field is it compressed or decreased? Is the distortion and the aberration still less since I am still using the middle portion of the lens only right?

Please correct me I my numbers above does not fit reality, I have since thrown my Physics books along time ago so I cannot be certain of this and don't know if I really want to dive into it. I just want to know if there is a free lunch somewhere in this execise.