If you don't need off road or heavy towing ability, the minivan wins on almost every issue over a vehicle like the Suburban or Expedition. Lower first cost. Better mileage. Less maintenance. Easier kid hauling (sliding doors are really awesome). Ease of access with low floor. More interior space. Car like handling. Utility - I have gone on cross country road trips with 8 people comfortably in our Odyssey, and also used it to carry 12' lumber or stacks of drywall.
Biggest downsides to a minivan are lower ground clearance, lower towing (although decent) and the tend not to have AWD. If you live in an area that gets snow, take a bit of your $15k savings over the Suburban and get a set of snow tires. Snow tires combined with modern stability control pretty much makes up for it.
Three row SUV's like the Pilot or Highlander are nice and give you that SUV image that everyone loves, but they simply aren't as practical. Worse mileage, higher cost and less interior space. Back row space isn't great in these and while using the back row, you are left with little luggage space.
Consider the Odyssey along with the Sienna. Both are very similar in cost, features and reliability. Sienna has a slightly cushier ride, while the Odyssey has slightly sportier handling. Sienna is offered with AWD, but those are rare.
Another interesting factor, Unibody minivans like the Odyssey are safer in crashes than full size body-on-frame SUV's like the Suburban per NHTSA. People think the opposite and feel safer in the larger Suburban because of the huge size, but the feeling isn't fact based.