You can tow about eight times what you can haul. This is because the typical tongue weight of a travel trailer is about 1/8 (12.5%) the weight of the trailer.
Now, COMFORTABLY towing is a whole other question, and has nothing to do with capacities or safety. If you load a 15-series pickup truck up to its maximum and start traveling with any regularity, you are going to get sick of it quickly. It's going to be frustrating and stressful to drive after the newness wears off.
Read some posts from people who have upgraded to the heavier trucks. Most claim a night and day difference, no comparision, why didn't I do this sooner, etc..
Whatever you do don't start out with a maxxed-out rig right out of the gate.