I have both and each has its place. That said, I use my 5Diii at least 90% of the time. I love what a crop format can give me when I'm doing nature photography. However, the 5Diii has certain advantages over the 7D and I find these to be really significant.
1. Superior autofocus. I generally use just the center point for nature photography. The 5Diii acquires the target much faster than the 7D and that's a huge advantage for subjects such as birds in flight. Its autofocus is also considerably better in low light situations than that of the 7D.
2. Vastly superior performance at higher ISOs. I routinely use my 5Diii at ISOs of 800-1600. I wouldn't dream of doing that with the 7D. For me, the 7D is a 400 ISO or lower camera. At ISOs above 400 with the 7D, noise, particularly background noise, is intolerable.
3. Better dynamic range. The 5Diii seems to capture a broader range of lighting than does the 7D. That's subjective, I know, but it just seems to do a better job. It also does a better job for me if I photograph something against a strongly backlighted background. With any camera that's often a recipe for an underexposed subject. With the 5Diii I can pull up far more detail from such underexposures than I ever could with the 7D.
I'll be curious to see whether the 7Dii catches up to the 5Diii in these areas. A crop format camera that handles low light situations as well as the 5Diii does and that has the 5Diii's autofocusing capabilities would be a nature photographer's dream camera, I think.