Here is my take on it. You're going to be driving each option, so you're going to be sitting in the truck for the 4,000 odd miles of the round trip. That's around 60 hours, a week on the road each way. That's 14 nights in a hotel, eating out three meals a day, and I figure the cost difference between that and camping at $100 per night, so the hotel trip will cost around $1400 more than camping (including fuel difference for pulling the trailer). Plus you get to sleep in your own bed, eat your own food that you prepare, etc.
Downside of camping is that you need to tow the trailer, you need to do the housework of maintaining the trailer, making the bed, doing laundry, cooking, washing the dishes. Figure two hours a day on housework and taking care of the rig.
Other things - you can be equally "free" with either. I often stop for an over-night tucked in the back of a truck stop - free, use the truck stop facilities, have a meal in their restaurant, shop at their store, fill up with fuel. I stop at a "camp ground" maybe one night in three on a long trip. When I do a long trip with hotels, I pick up the State visitors guide at the visitors center when I enter each state. It has nothing in it but discount coupons to all of the hotels and motels along the interstate, exit numbers, other amenities, and I use that as a guide to where I plan to stop each night. Makes me equally free. So I've done trips each way, and enjoyed both. They are quite different, though, and I sure do get tired of hotels and restaurant food after a couple of days on the road.
Brian
2005 F250 Supercab, Powerstroke, 5 speed automatic, 3.73 gears.
20 ft race car hauler, Lola T440 Formula Ford, NTM MK4 Sports Racer
1980 MCI MC-5C highway coach conversion
2004 Travelhawk 8' Truck Camper