Agreed about both taking very good pictures. The 7D under the right conditions performs just as well as its expensive brother. On the other hand, much of the advantage of crop in giving extra reach is illusory. I did some iso12233 chart tests at 100 iso with the 100-400mm L on both bodies as it is a very popular but not very sharp lens - its defects according to Plamen's analysis should show up more on the crop. At closer distances where the closely spaced lines on the chart are easily resolved, the 5D III gave clearer, more contrasty images. At long distances where the lines were at the limits of resolution, they were marginally better resolved by the 7D but IQ was much poorer from poorer contrast and so again the resultant overall image was not better.
The good news for the bird photography 7D owner is that you have camera that can equal the best (at lower iso).
The good news for the bird photography 5D III or 1DX owner is that you are not really disadvantaged by not having the crop factor (but both owners probably don't need me to tell you that).