My wife and I swore that we would never own a minivan, but our third kid pushed us over the edge. We ended up getting the Sienna based on previous good experiences with Toyota, and the fact that we wanted all-wheel drive (our driveway is a nightmare in the snow). We researched the Honda as well and truthfully you can't go wrong with either choice. If you want more cup-holders, however, get the Honda it's got 18 or something like that as opposed to the Sienna which only has 14 or so - these things are important.
As much as I thought I'd hate the thing, it's not that bad. I think the dreaded word here is practical. We looked at SUVs with third row seating, but they are a bit cramped, unless you get a Suburban ($$$$). My wife drives it most of the time, but there's no "Mom's Taxi" or soccer ball decals on it - we haven't gone that far off the edge.
We've managed to put at least one dent in it for every 5000 miles so far - hitting deer, garage door openings, mailboxes, etc., so it looks a bit worse for wear. Even after a year I still catch a lot of shit about having the thing as I was rather vocal in my distaste for them - karma, I guess.