We've been to both and prefer the North Rim for the scenery, trees, deer, less people. What I didn't read here is that at the North Rim, not only do you have access to camping within the park, but there's a Forest Service CG on the road between Jacob Lake, another at the junction and a full service RV park near Jacob Lake - Kaibab Camper Village. Well worth the stay. A little tight but you can get in there and it's in a beautiful grove of trees.
Here are a couple of pictures of the Kaibab Kamper Village and what the forest looks like at the North Rim.

