For farming, BM has distinct advantages in the form of Black Ox Statue. Farming spots like the Murloc Cavern (pre-nerf) are fantastic with a BM monk. As the expansion goes on, more of these should pop up so you could get some use out of it. Personally, my biggest issue with farming at 101 is the lack of valuable BoEs, but if someone found a quick respawn high value mob spot I think Brewmaster would be king.
PvP uses for 101 twinks are off the table as far as I know. Stats in all battlegrounds are standardised to level upon entry, your gear makes no contribution.