If you want tourist and all the hype that goes with it do the South Rim. If you want to do doon-docking and see the Grand Canyon and see more or the terrain and scenic do the North Rim. IMO it is much more scenic without the hype and tourist trap stuff. Go back into the park to do your camping. Gorgeous!
FYI, personally we tried the CG at the front of the north rim (Jacob Lake CG) would not do that again. We go back into the park and boon-dock.
IMO Bryce is more scenic than GC but it is small and can be done with a one night stay to catch a sunset and sunrise.