An AWD crossover would give up some of the interior flexibility due to the drivetrain but would bump your tow capacity up to the 4500-5000 range. From a driving comfort standpoint they would be about the same, but with larger tires and a bit more ground clearance they can be a little more flexible in terms of where you can take them. Obviously they're still pretty limited in that regard but they would still be an upgrade compared to a minivan.
We towed a 3500 lb pop up quite a few miles behind a 2010 Pilot with no WDH and it was a well matched combo (4500 lb tow rating). One thing you'd want to check out is whether you even can use a WDH with your tow vehicle. I'm pretty sure our Pilot's manual says not to use one.
