Actually the BB will rise to 12.3 inches. 650b axle height a 1/2 inch difference to a 26 inch wheel with the same tire model.
A higher BB raises the rider and bike weight center. There is more pedal clearance, a benefit for pedaling rocky and rooty trail. But side to side response is theoretically slowed, although I personally didn't notice any loss in cornering ability converting my bike to 650b, only the improved grip, rolling ease, and added stability overall.
Without changing wheelsize a lower BB is more stable, and easier to handle and climb on smoother trail, and rocky downhill when not pedaling.
BB height is personal preference, mainly depending on trail conditions. Rocky trail riders usually prefer higher BB's than common.