I actually have both of the smaller versions, so the BM 556 and the Buck Vantage Pro small. Personally I prefer the 556 even though the Valox scales are not as nice as the G10 on the Buck.
The reason why I prefer the 556 is because I have had less issues with it in general. The blade profile works just great for the minor cutting I do and it seems to take an edge decently on a sharpmaker even though I'm pretty mediocre at sharpening. I also really like the Axis lock for just being so easy to use and close without having to put my fingers in the way. Also, even though the scales are not as nice as the ones on the Buck, they are really grippy for plastic scales and at least for my hands, the checkering and jimping seem to work fine without causing too much irritation.
Personally, my Buck Vantage Pro has had some issues which keep me from carrying it as much. The steel is really nice and the blade is a nice cutter, but the other aspects kind of ruined the knife for me. The G10 scales feel nice but are pretty slick from the factory, and I've had some grip issues just from having sweat on my hands. The flipper for this knife is too small for me and doesn't really work unless I wrist flicked the knife open. I also had some pretty serious issues with the lock, where the liner pretty much started off in the middle of the knife and worked over to about 3/4 to almost full engagement. A couple of times, the lock would actually get stuck on the wrong side of the blade tang, and I had to pry it back using a SAK.
These are just some of my personal experiences, but hopefully it works out better for you. I would definitely check out the Buck in person or have someone check it out before buying one though and I fully recommend the BM Griptilian series for being a pretty good knife.