Now this is a very tough call.....too of the finest of each of the finest companies....the creme de la creme and so on.
But...I think I'd take the 710. It looks classier, has the superior lock and I like the blade shape more.
The Military is thin and light, where the 710 gives you the feeling of a tank. I can see situations where either would be nice.
Plus the Military wins in longevity, I've heard the axis lock spring on the BM can wear out and break, although none of mine have yet.
Liner locks wear out much faster than axis locks, on average anyway. I don't know about the Military, but I suspect this would be true as well. Out of the many thousands of axis locks that pass through this forum, we've had maybe 20 springs break and one, maybe two, failures.
Given that, it seems to me, since we've been using probably in excess of 5000 axis lock knives on this forum alone, for many years (and we flick our knives all the time), is very impressive to have such a low failure rate.
I think, in reality, liner locks have a very good failure rate too (from reputable companies, that is), and are quite underrated. But still, no comparison to the axis. If we saw thousands of cheap axis lock ripoffs from the low end companies, then we might see the same increased failure rate.
Anyway, you can't go wrong. These are like the company's greatest hits.