I found both PB and BM to be almost identical in this portion of the class. For seat work I really enjoy the PB way of teaching because they really emphasize that the movements come from your seat (butt) not your leg, which wasn't really emphasized with BM instructors. Since I'm an old pro, I knew where to squeeze from - totally kidding!
Part one against the wall: Again this portion of the class is very similar with both. The biggest difference being the emphasis on breathing with BM. The deep breathing comes from your diaphragm which helps shape those pesky six-pack abs!! Also once the wall session is complete you go into another round of push-ups!
I like to think that stretching is pretty hard to mess up, but when I was in the BM classes, the instructor would always correct my hip or arm placement and I have to say it made the stretches feel like they were going much deeper! In both PB & BM you stretch after each section, but there was much more emphasis on the bar in BM. I felt like a ballerina in one part of the class because you lift your leg onto the bar to really get a deep side and leg stretch in - I'm not the most flexible, but it worked!