There are good transit connections from Logan airport, but you'd still have to board them. I wouldn't want to walk anywhere from the arrivals terminal on foot. Walking out of South Station is pretty nice though, lots of places I'd want to be nearby.

Billy Bishop is pretty convenient, I think it's quite unusual in that respect. But for the same reason, it's rather controversial and limited in the airplanes it can take, and its future is often in doubt.