I'd say the BM710HS. The AXIS lock is superior, in my mind, to a liner lock. You can open and close a 710 faster, the AXIS lock is stronger. You can wear the 710 left or right carry and operate the lock in either hand. The 710 also has full dual steel liners. It's a solid knife, and has a nice slim profile.
That said, the Military has a better blade. The blade design on the Military is going to slice through things better. Also some people prefer the handle on the Military as it offers a good grip.
For a hard use knife that I know I'm going to use frequently I prefer an AXIS lock. I have a Spyderco Starmate which is similar to the Military as far as construction of the handle, pivot, lock, etc, and I never carried it. It's a great knife, but I found the 710 to be more user friendly, and I have more confidence in it's construction.
I'd say try and handle both and go with whichever feels better in your hand and pocket. Also check out the BM Doug Ritter Grip.