If you go for the home mortgage based Suburban, for double the price it does have many advantages over smaller minivans.
If you're going like for like in this comparison, IE Highlander/Sienna, Pilot/Odyssey, Telluride/Carnival, etc, the SUV's have a sportier feel while having a lot less space and utility than a minivan. I mean, who doesn't love rear seats with absolutely no real leg room that also hog nearly all the luggage space? But the good news is, you don't have to cop to driving a minivan, so there's that.
But if you don't need all the extra space and utility of a minivan, the SUVs do tend to drive better.