They weigh almost the same amount - 593 grams for my NMSFNO vs 606 for my BWBM.
The BWBM handle is less comfortable. My NMSFNO has hand-shaped micarta mags. There are no hotspots or anything on the NMSFNO when I chop, but the BWBM does give me Busse Pinky (not nearly as bad as the fusion mags on my FSH though).
The BWBM is a more efficient chopper. The greater length and thin edge profile contribute to deeper bites and it's less tiring to swing.
For batoning, both have their strengths - the BWBM's greater length will allow you to split larger logs than you could with the NMSFNO, but the NMSFNO's thicker, beefier profile will be a better splitting wedge for splitting wood more easily with fewer swings.
For brush clearing, the BWBM whoops the NMSFNO's butt. It swings a lot more like a machete, and takes down thin stuff like nobody's business.
Of the two, I find myself preferring the BWBM. I'm going to pair either of them with a small knife for detail tasks anyway, so I might as well get the greater length of the BWBM for machete like tasks and better chopping. I am, however, tempted to re-shape the butt to a more NMSFNO-like profile, as well as adding my own, thicker slabs.
Also, my NMSFNO is a superior color