I can't give you the best comparison as I have never put that many people in a Suburban for a long trip...but I can give you a few pros/cons of each.
My grandfather owns an 08 Grand Caravan in pristine condition with about 35k miles that sits in the garage until a family vacation comes up, most being 3-4 hour trips, but the occasional 16 hour or so drive to Florida. Everyone in the family fights over driving and riding in it on these vacations, that we take multiple vehicles on. Milage when packed full with 4-6 people and loaded down with luggage is typically around 20mpg on the highway and is an extremely comfortable ride. I can say the space and comfort is loads better than the 06 Durango (newer, larger body style) my parents owned for a short period of time, not quite comparable to a Suburban but similar to a Tahoe.
My experience with Suburbans is mostly in the Fire/Rescue environment, where the 3rd row has been removed to make space for command boxes, etc. The 2nd row is definitely tight even in these, especially with 2-3 men in the back. They are great for our use because we run 3/4ton Suburbans capable of handling these large storage boxes, having 4x4, a larger motor, and capable to tow quite a bit more than a minivan or even a half ton Tahoe/Suburban.
IMHO, if I were going on a trip like you described, I would opt for the minivan. However, given what you described, I am sure that the Suburban would work, but I do not think it would be as comfortable as a minivan.
Kyle