Long wheelbase is a huge advantage. If going with a full size SUV such as a Suburban this doesn't apply.
If you are shopping new off the lot, I think it's likely you'll find more pickups with tow packages than SUVs with the tranny cooler and 2" receiver.
The "light in the rear" nature of a truck results in less squat from tongue weight, and if you need some lift there are more choices for restoring level with a truck.
The interior of a crew cab truck can be just as luxurious and comfortable as any SUV, and with a bed cover you have just as much covered storage.
But it all comes down to what you like. Just don't believe what the salesman tells you about towing. Half would probably tell you an Escape or Rav4 could haul a 5th wheel.