Quite a while back, I formally tested the 5DII vs. 7D, and came to the conclusion that there was no significant IQ difference between an image taken with the 7D and an image taken from the same distance with the same lens (100L) on the 5DII, then cropped to the FoV of the 7D. The only difference was that the 7D image was 18 MP, and the 5DII image was just over 8 MP - so, if 8 MP is sufficient for the intended output, there's no advantage to the APS-C.
Note that I'm comparing in a 'focal length limited' scenario - if you fill the frame with the subject on both cameras, the FF is the clear winner (compare the 7D to 5DIII
or 7D to 1D X
with the frame filled, i.e. closer with the FF)
More recently, I tested my 1D X vs. 7D with the same motive as yours - use with a 600 II, considering teleconverters as well (and the ability to AF at f/8 vs. f/5.6 on the 7D). Comparing at the same focal length (bare lens or 1.4xIII), at low ISOs the 7D has a very slight advantage in terms of IQ. But that advantage is offset by the better AF of the 1D X (shared by the 5DIII). As you raise the ISO, the 7D is the clear loser - to me, that's a key factor, because at f/4 or f/5.6 with fast subjects, you often need pretty high ISO. I can shoot the 1D X at ISO 6400, and it looks better than ISO 1600 on the 7D. Again, the caveat is that you have fewer MP in the final image from the FF camera if you're cropping. But 7-8 MP is enough for decently-sized prints (16x24"), so I'm fine with fewer MP.
When you factor in the 2x vs. 1.4x TC to maintain AF, you need to crop the FF only slightly to achieve the same FoV as the 7D. In that case, the IQ advantage of the FF is even greater and evident at lower ISOs, and that's despite the bigger optical hit with the 2x vs. the 1.4x TC (note: this is on a MkII supertele - I expect the results would be different on a lesser lens, but the MkII superteles take the 2xIII very well).
Like you, I had the 7D and 5DII combo, the former used for birds/wildlife/sports, the latter for pretty much everything else. After getting the 1D X, I have come to the conclusion that my 7D is superfluous. Perhaps worth keeping as a backup camera, but else mainly a paperweight.
Hope that helps...