We have been to Yellowstone and the Grand Tetons three times since 2007.
We love both. This is what works for us.
We usually come in from the South and spend two or three days in the Grand Tetons, Colter Bay RV Resort, FHU and close to the marina.
From there you can visit the park and go to Jackson Hole, take a cruise on the lake.
From there we travel through the South Entrance of Yellowstone and out the West entrance to stay at Grizzly RV Resort, FHU and close to the town and the park entrance. From there you can go into town and eat out or shop. Grizzly also has a laundry.
When we visit Yellowstone we spend very little time at the RV and most of the time visiting the park, so I don't want to have to deal with running the generator or keeping the batteries charged.
This is what works for us. You can check our blog for more details.
IF YOU ARE STAYING AT EITHER OF THESE PARKS MAKE RESERVATIONS NOW. August is a busy time at the park. ENJOY!