Both campgrounds have water and a dump station available, but no hookups.
Cottonwood is now being run by the Navajo nation and not NPS. My understanding is that there is now a camping fee.
Cottonwood is closer to Chinle and is well shaded with large cottonwood trees, clean restrooms. There is a cafateria across the street from the campground and tours of the canyon can be set up at the lodge.
Spider Rock about 10 miles east of Chinle on hwy.7 the south rim road and is privatly owned. Tent sites are $10. and RV sites $15.
The closest place to the canyou with full hookups that I am aware of would be Ganado.
We have stayed at both and never felt unsafe.