Hello Bushcraft,
Hard to compare them as they are so different.
The CPM 3V steel on the Bark River LB makes for a very long-lasting, durable edge. It is more rust resistant. The LB is heavier and thicker. The LB handle is narrow contoured but with thick, filling slabs. The edge on the LB is a convex-scandi, although it is a very thin convex, barely a convex. It cuts like a scandi should, although I believe the BHK zero-edge has an extra, slight amount of bite. The LB primary bevel is well placed so it can rest on the cutting surface and cut.
The BHK makes for a slightly more traditional carving handle, in that it is not heavily contoured, just full and rounded, allowing for more play and those awkward grips for hard angles. Granted, the LB is very comfortable for carving, no hot spots. The thick spine makes a great push cut platform. The BHK slabs taper towards the ricasso making it better for choke grip than the LB. The LB has a slight integrated guard and a steep drop from the slabs at the ricasso making choke grip somewhat uncomfortable. This, for me, is the main fault I find with the LB. They are both great carvers, but I would tend more towards the BHK for extended woodcraft periods.
The LB may has an advantage in terms of bushcraft in that the blade is longer and the convex edge has a bit more steel behind the edge for added general-use strength. The LB would make for a slightly better deep hole driller with the narrow point.
The BHK has more belly making it a better hunting use blade than the LB. It will also have an advantage in hollowing out bowls and food prep/kitchen work.
They are very different scandi's, but I love them both, and each has their place and advantage to certain occasions.:thumbup:
So far, the BHK has been winning it out on overall use and open design comfort... The Bark River LB, on advanced steel and strength.
Hope this helps!