I'll chime in. We currently have a 2005 Sienna with 230k miles and I have owned a 2005 Odyssey as well. I prefer the Odyssey in general, but it was crashed early so I have more experience with the Sienna. My issues with the Sienna:
1. 2004-2005 have an issue where the VSC/ABS kicks in unexpectedly. It SHOULD be a safety recall, but Toyota is waiting on someone to get killed I guess. On freeway interchanges and onramps it thinks you are skidding and applies ABS to straighten you out. Sometimes towards a concrete barrier. Replaced steering rack, yaw sensor, etc, but never was able to fix it. Probably a result of squishy rubber in front suspension. Ultimately disabled ABS/VTC to avoid the issue. Not a huge deal in areas with little rain/snow like mine, but I wouldn't recommend it and I hate it for a car my wife/kids ride in. Look it up on NHTSA if you want more info.
2. Eats front tires and brakes pretty quickly.
3. In 5 years/60k miles replaced: battery (twice), alternator (twice), brakes (twice), radiator, steering rack, starter, sliding door hinge, sliding door motor, thermostat housing (broke due to heat).
4. We got the XLE with lots of electronic toys that break. Laser cruise control and parking sensor system do not work.
The engine is reliable and just works. I keep waiting for it to die, but it just keeps going.
I'm looking for an Odyssey to replace it, but based on comments here, I might look into the Mopar for parts prices.
One last tidbit, our 2005 Odyssey took a solid 30-40mph rear-ending while sitting still. Destroyed the car that hit us, but I just popped the trunk, threw the rear bumper cover in, and drove home. I had just upgraded from an Accord and had two little kids int he car so I was very happy with how it handled it. My wife still prefers the Honda in terms of feel.