It's a total judgment call.
I own and use and love both.
The difference between the steels is not significant enough to make much of a difference. D2 will be more stain resistant, M2 will be a little tougher. All other things being equal, I'd prefer M2 because I find it much easier to sharpen and I think I can get a better edge with it. This reflects more on my sharpening skills than the steels though.
Oval hole vs thumb studs - total judgment call, whatever works best for you. I find the 710's thumb studs to be easier to reach than the 806's oval hole. Others will have the opposite experience.
Blade shape - I find the 710's blade to be the most useful I own, but there's nothing the AFCK won't cut that the 710 will.
Handle shape - for the same size blade, the 710 has a smaller handle, and should leave a smaller footprint in your pocket if that's a concern. The AFCK has that pointy butt for pommel strikes. I find the AFCK's handle to be among the most comfortable and secure out there. The 710 is comfortable, but not as secure, in my hand.
For me, the 710hs is the better utility knife, because that blade cuts so well, and the 806 is the better defensive knife, because of the handle security.
My ideal Axis lock would be a 710hs blade in an AFCK handle.
The best way to decide which of these knives is best for you is to go to a knife/gun store/show and handle them both. Once you have both in your hands, side by side, you should be able to decide which suits you better.
You're lucky, though, they're both such great knives you can't go wrong.
Let us know which you decide and how you like it.