Minivans have an old and untrue rep. It's supposed to be the vehicle for "soccer moms". Well, aside from whether there's anything wrong with being a soccer mom, it's not true anymore. A SUV is the "soccer mom" vehicle now. The great majority of SUVs aren't even "real" SUVs anymore. They're basically station wagons or minivans without the sliding door. They don't even look tough or rugged anymore.
As a parent, we tend to be more practical. The minivan really is the most practical vehicle for a family that needs more space than a sedan (and doesn't tow a lot). You need to jump up to a monster vehicle like the Suburban to match the people and cargo carry abilities of a minivan, even tho the minivan is smaller than a Tahoe. Plus those sliding doors will make your back thank you if you still have small kids in car seats.
Look at the new Pilot, for example. Gone is the more rugged, boxy appearance. It looks just like a minivan now, but it lacks the sliding doors, interior space and flexibility of a minivan. You typically pay more for the Pilot and get less in terms of kid and cargo friendliness. About the only reason on paper to buy a Pilot over an Odyssey is for the small percentage of people for whom snow tires aren't enough and genuinely need AWD and don't mind the loss in fuel economy.
And this is from someone who drives a midsize SUV;-)
To get a vehicle with more interior and cargo room than Odyssey, you do have to go with a Suburban or Expedition EL or equivalent. And even those models are arguably less kid-friendly in terms of seating and access. On the plus side, they do offer true 4WD, off-road and towing capability for those who need to do this frequently. Of course, for the considerably higher cost upfront and for fuel, you could rent one for a couple weeks a year every year and still come out ahead. And like msg221 said, the Odyssey handles better than any of the full size truck-based SUVs, which is important if you are mostly driving in crazy urban and suburban traffic. Not to mention Odyssey's great crash test results and safety features! Sienna and Sedona are good choices, too!