We have been to both rims and we liked the South best. The KOA near Williams was nice and we used it for our home base. From there I think the Canyon is only ~35 miles or so and Williams is closer than that. We did the train ride from Williams to the GC and really enjoyed it. We did a lot of roaming around when there to various towns and places. I cannot remember the name of the peak but we went to a ski resort and rode up the mountain which I think is halfway between the KOA and the GC. It was early August when we went and it was really not that bad people wise.
It really depends on what you want to do.