Two Hands wrote:
Yellowstone is big, big, big. Seven days would be good for Yellowstone. But if you only have seven days for both and want full hookups I suggest Fishing Bridge RV Campground in Yellowstone for four days and then three days in Colter Bay RV Campground in Grand Tetons National Park. One goes to Yellowstone for the scenery and wildlife viewing. Not necessarily for a great camping experience. Have a great trip.
We'd highly recommended the above, also. In addition, if you move between the two parks during one week, you could easily do without hookups for 3-4 days at each park. You'd have many more choices that way. We'd also recommend you stay IN the parks themselves for the best experience and shorter drives. The parks are huge. Any of the campgrounds within the park are great unless you want a 5* resort. Besides, the parks should be your experience, not the campground. You won't be in the campgrounds much anyway.