If I remember correctly, the REKAT lock went to near 1000 in-lbs of torque (or leverage or whatever) before it failed. Something along those lines, tested by Spyderco on their "Destroyer". Went the heaviest of any lock they had tested up to that time, again IIRC. They have not tested the BM Axis, though I kinda doubt that it would go that heavy. So, to answer your questions, to the best of my knowledge, in reading as much as I can in the forums here, it is the strongest made. Period. I'm sure there is someone out there who could defeat it; you probably wouldn't care, as he could probably break you in half anyway.
It is not the most elegant. Read a while, and you will read that the action tends to be gritty and stiff, at least until it is broken in. Maybe better afterward. Someone over in the general discussion forum posted doing a "real-world" test where the REKAT lock was tested alongside a couple other knives, in conditions that included extreme dirt/mud. IIRC, the REKAT was most susceptible to fouling by the mud and not locking up reliably. So, don't drop it in the mud. If you do, rinse it....
I have a couple of Axis locks. If I had it to do over, one of those would be a Carnivour. But, it wasn't made yet, so....
Bottom line, from everything that has been said so far, at this point in time it appears to be the strongest. As far as pure strength, though, there are probably a lot of locks out there that you couldn't break without a machine. Reliability plays an important part as well. A lock that un-locks when you aren't expecting it, even if you are only putting 40 in-lbs of torque on it, will cut you enough to need stitches. I would say that both the REKAT and the Axis are the most reliable locks at this point, with a slight edge going to the REKAT. I would definitely recommend handling both if you can, before buying one.
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Work hard, play hard, live long.
Outlaw_Dogboy