OP seems concerned with high ISO and noise so the 70D might not be the best choice of the three. Even the 1D3 leads the 70D in that regard and only very slightly behind the D7100.
http://www.dpreview.com/reviews/nikon-d7100/22
Use the above link to compare D7100 and 1D3 RAW high ISO, 1D3 is not less till its max ISO 6400.
But the D7100 is still slightly better at "high" ISO (even at ISO 1600 when you equalize FOV). No biggie as the dif is small (.2 stops measured)
Also should consider color and tonality in high ISO where 1D3 is very nice even at ISO 1250.
Why? He didn't really seem concerned about that, especially at low ISO's of 1250 (relative). Color and tonality are so subjective and so easily adjusted in post that minor dif's in accuracy and saturation from manufacture default seems of little consequence except for the no PP JPEG only shooter.
I am not convinced APS-C cameras today can deliver those clean photos even an old 1D3 can do, other samples at ISO 1250 from someone else in eagle in flight.
http://www.dpreview.com/forums/post/30655674
I can see 1D3 color tonality in airshow photos.
http://www.dpreview.com/forums/thread/3238329
But the D7100 is still a .4 to half stop better at high ISO/LOW noise. Fact is Fact
I don't see much difference in above DPR lab samples so that difference is pretty small.
Agreed.. .2 and .4 respectively. Only a player if he's printing large or cropping heavy.
All today's APS-C cameras don't do well print large or cropping where FF cameras are much better. Please don't exaggerate.
However if anyone watches that video (link again below) that is reviewed very fairly in an excellent review, 70D is an obvious better choice in speed, AF accuracy and tracking, overall response, video, touchable LCD.
He doesn't really seem interested in the 70D so much. In terms of pure IQ, it really isn't a step up from the 7D. He seems more interested in ISO performance and other IQ aspects of photography.
I don't get it. His only concern is 70D's price. However 70D and D7100 have almost the same price. If he considers D7100, logically he also should consider 70D. 1D3 is really in a different category.
Seriously the benefits from 70D in other areas I mentioned are much bigger than small difference in high ISO and noise between two cameras. 70D is more useful camera overall. Only FF cameras have significantly better high ISO and low noise and overall IQ (sharpness, color tonality, clarity and high ISO).
If OP really want better high ISO and less noise or landscape or portrait, FF is a much better option to get a EOS 6D which only cost little more or D6100 (that costs more). The difference among today's APS-C cameras are very small.
True, some big differences in resolution and DR within APS-C... but modern FF holds the Lowlight/High ISO lead.
Sorry I don't see big difference in resolution (20 vs 24mp on APS-C) as they don't do well both in big size print (such as to 20x30") or view at full size on monitor (such as view at 3000-pixel wide and most view even in smaller size in their 1080p monitors), or DR (only if you severely underexpose photos but no much difference if expose normally) between Canon and Nikon APS-C cameras. Only FF cameras are much better in IQ. 6D doesn't cost much more than D7100 and 70D but gains significantly in IQ.