I have both and find both to function about the same.
I bought the BK2 first, and immediately got the aftermarket micarta scales (I know...plus $40 almost equals cost of base Esee 5). I have larger hands, and didn't care for the "slickness" of original scales, although the ergos were excellent. I planned to do this before I purchased it. At the time of purchase, the BK2 sheath was the one that tended to dull the blade when removing it from the sheath ( has since been corrected). I was aware of this as well, and had a custom leather sheath made by Skystorm. Got that sheath about a week after the knife.
I was also aware that it was not going to be a good slicer, and my intended use was to be mainly for wood processing. I put a convex edge on it, and it is now my field "axe" (when pack space is limited). I've had excellent results with splitting/batoning. If I have room in my pack, I will carry a hatchet or small axe. In either case, I also carry a folding saw, and my Survive GSO 4.1 or my Bark River Bravo 1. The smaller knives are for any bushcrafty things like feather sticks, shavings, and any misc camp chores that my folder can't handle. The BK2 is a tank of a knife, but if you are aware of it's pros/cons, and decide what you REALISTICALLY need it for, its a great investment for the money.
I bought the Esee 5 as a back up / alternate to the BK2. Both fit in my leather sheath. When car camping or at the cabin, I generally have both, and often hand of 1 or the other to another person to help with wood processing. Batoning seems to be a safer and easier process to get a hang of, for those with minimal hatchet/axe experience. Plus, it's fun to see people's reactions when you start "splitting wood with a knife", and they've never seen it before.
While I prefer the ergonomics of the BK2 handle, if it came down to a choice between the 2, that would depend on the situation. Heading to the woods in a SHTF scenario? BK2. Making way through an urban environment in a SHTF scenario? Esee 5.
Both are great knives and cost is close (if you upgrade the BK2 with micarta scales). Buy 1 now, and put the other on your birthday list.