You said you shoot sports and BIF. The 5D3 has a smaller buffer than the 1D4, which could be limiting if you do a lot of continuous shooting.
Since you shoot subjects at a distance, you might want to consider this...
The 7D2 has a smaller fov than the 1D4 (1.6 vs 1.3 sensor size).
A 400mm lens on the 1D4 would produce the same fov that a 520mm lens would on FF.
A 400mm lens on the 7D2 would produce the same fov that a 640mm lens would on FF.
This may or may not be important for your type of shooting.
If you crop the 1D4 image until it has the same fov of the 7D2 (any mm lens), you'd be left with a 10.6mp image.