Truth is. for a 20' TT, any full size SUV will work fine. Just get enough motor and rear gear. Be sure to properly adjust the hitch, and you will be good to go.
Yes I have experience towing with a SUV. We towed our 27' TT with our 2002 Expedition for years. It did a great job. No sway, and plenty of power.
Advantages of a truck, are that you can just throw the wet stuff in the back if it is raining when you break camp. Also you can carry firewood and bikes in the back.
It is your choice. Either will do what you want