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Sigh.
Years ago Detroit got rich selling land yachts that had only two doors because a large segment of the population thought 4 doors were "uncool". Nevermind that the 2 door land yachts were impractical -- the back seats were hard to access and the huge doors made it hard to get in/out in parking lots.
Today that same segment of the population forgos the minivan for the SUV.
Compared to the pseudo-SUVs the minivans win hands down on every point. More space inside? Check. On the cargo side, you win both with volume and with area -- with the Odessey and Sienna you can even fit 4x8 sheets of whatever in the back. On the passenger side your 3rd row is much more accessible and roomy. And the lower floor means you have enough floor-to-ceiling space to actually move around if need be in the back.
Gas mileage? The minivan style wins against the equivalent sized pseudo-SUV. Drivability? The minivan has a lower center of gravity which makes for much more stable driving, especially in icy/snowy conditions. If you absolutely, positively need AWD you can also get that in a minivan. Access? Young kids can get in more easily with the lower floor (and are less likely to injure themselves falling on the way out of the car). And the sliding doors are a boon in tight spaces like parking lots. Off-road? C'mon, the pseudo-SUVs are a joke off-road. The minimal extra ground clearance may help slightly in some situations, but generally is useless.
Compared to the "real" truck-based SUVs (i.e. Chevy Suburban, Ford Extinction, etc) the minivan wins on almost every single point. Gas mileage? Slam dunk for the minivan. Interior space? The most monster of the SUVs have more cubic yards of volume, but the higher floor means that it's less usable for most cargo. Plus, the higher floor makes it less friendly for passengers as it's harder to move around inside.
Drivability? Here's where the "real" SUV myth explodes. The Ford Extinction class of SUV is three times more likely than a mid-size sedan to be involved in a single car accident. That's because they are inherently unstable. When the snows hit where I live the first vehicles off the road are the Extinction class and the big Pickups. The higher center of gravity makes them far less stable in any driving condition, and the rear-wheel drive makes them susceptible to tailspins (even those with AWD still have most of the power in the rear wheels, so spin outs are common on ice).
The Extinction does have two advantages -- towing capacity and it does better on heavily rutted farm roads (which few people ever drive on). They aren't good for serious 4WD roads, of course, although I'm sure most owners don't know that. In terms of towing, even the Sienna can pull 3500 lbs in a pinch -- and honestly most towing jobs above that are due to lifestyle choice, not anything approaching necessity.
In the end, if you have to have a car with that much seating the minivan is the practical choice. We have an aging Chrysler which we intend to drive forever. We use it less than 5000 miles/year -- only when the hybrid is not an option. It's worth about $4k on the auto market. Something to consider.