Here's my $.02....I cried when my 2000 Olds Silhouette died at 140K and we looked at the Odyssey and Sienna. We've got 4 kids and I needed a full sized minivan, so the Nissan Quest was out (not enough cargo room in the back). There were 2 things that made me pick the Sienna LE over the Odyssey:
1. The remote button for the sliding doors. In the Odyssey, there is one button to the left of the steering wheel, and only the driver can access it. In the Sienna, there are buttons in the middle of the overhead console and on the wall of the van between the front door and the sliding door. Much more convenient.
2. The outlet for charging phones, etc. In the Odyssey, it was on the center console (where the radio, etc. is located) at the bottom, practically at my feet. In the Sienna, it's on the same console except at knee level. Again, more convenient for me.
Only two things, but for the number of times I need to use those two things, there were the deciding points for the Sienna. As for recalls, I've had one for a spare tire bracket. It rides great and gets decent gas mileage - typically 22 mpg, and that's running around town for my kids. It does slightly better on the highway. We've gone to Disney twice, and Niagara Falls. There is plenty of room for 4 kids (ages 10 - 14) to spread out and room for 6+ suitcases in the back, and you can still see out the back window.
Odyssey or Sienna, I don't think you can go wrong. Best of luck!