Having one of each I would have to say the way the BP is built probably would keep it from saddling a branch like a GTP. The GTP really is a beautiful creature with an amazing build, the way mine can float through the branches is a feat.
My BP was climbing around the other night and decided to climb on top of a water dripper that hangs over her water bowl. She does this often but on this night she decided to fall off and belly flop in her water, she is definitely not as skilled as a GTP. I think she would need a really fat branch to saddle it. Then its more like laying, lol!