We had a 2007 Odyssey, totalled in an accident. We went shopping for a new van, between these two choices as well. First of all, I'll hedge, and say, both are fine minivans, probably the best two choices in this class (haven't driven the new Pacifica), either one will be a good choice.
We went with a Sienna a few years back, because we thought it was a little quieter, and a little roomier inside. Also, our budget at the time and choices led us towards a mid-level trim - we knew we had a baby who, with her siblings, was going through some "messy" years so we didn't want a brand new van. We'll be in the market in about a year or two for a new van, and right now my wife is in between these two choices again - our friends have loaded versions of both and are nice, so it makes it a hard decision.
There's a new Odyssey just on the horizon, and the Sienna is in need of a refresh, too - it has been essentially the same since 2010 (the 2011 model year launched early). The Sienna and Odyssey both had Mid-model changes, right now I'd probably lean slightly towards an Odyssey, but that's more based on features. Folks have already mentioned all the big differences otherwise, it mostly comes down to preference.
We had 125,000 + in the Odyssey in five years, and now have 120,000+ in the Sienna (most of them ours), and no real problems. The Odyssey needed basic maintenance (including t-belt and water pump), and wheel bearings. The Odyssey drove a bit sharper but the Sienna feels faster. Sienna likewise is mostly oil changes, filters, tires, although it does chew up brakes faster than we'd like. Both survived well through family life - kind of hard duty on a drivetrain and interiors.
