Post-Helios One Mojave Brotherhood of Steel is a toss up. If the Legion fights like how they usually do and just send waves and waves of troops like tactical idiots, BoS without a doubt.
I'm gonna add on to Azula's scenario, Legion are forbidden to use normal "chems" like Rad-x and Radaway, they would die of radiation and from Super Mutant Overlords, and whatever is left from their crap army would
get decimated by a fraction of Lyon's Brotherhood of Steel.
Still going on with the capital wasteland thing again eh? *sigh* some people never learn.
Anyways The Mojave BOS pre-helios vs. Legion. Legion would of course win. Look at how the NCR took over helios one. If the NCR can do it, the Legion could definetly do it. I'm not saying Legion would completely decimate then, no. They would probably lose quite alot of men, but would win nonetheless.