I researched, made pro/con lists, and test drove each (in different weather conditions on different road conditions) for several months before making my final decision. I was getting rid of a year and a half old minivan I had a lot of dislike for and I wanted to cover all my bases so I didn't find myself in the same situation later on.
I chose the Sienna. Mine is an 8-passenger, however, I do not use the 8th seat. It's not child seat friendly. It would be if it sat on the same level as the captain's chairs, but it doesn't, so it's not. I fit fine in the 8th seat (I'm petite), as would a child who 5-steps, but that's about it.
The Sienna is "taller" than the Ody (not by much in specs, but it's significant when you're inside the vehicles), which was a large factor for me because my oldest rides in a HBB in the 3rd row and needed "room to grow" in the booster. The 3rd row seats, headrests, and seatbelts were a better fit for my 8-year old. He will not be in a HBB forever and when that time comes, I need to know he'll fit well back there. Not only was he more comfortable with the Sienna headrests, but the seatbelt fit his body better, and he was closer to 5-stepping in the vehicle seats. Because I have 2 older kids (8 and 7), those factors topped my list.
The Sienna only has 3 complete sets of LATCH (each captain's chair and middle 3rd row), there are no "extra" top tether anchors. This was a non-issue for me because even if I have a 4th child, I will only have booster riders in the 3rd row. The 3rd row outboard headrests do not come off and do not adjust (they are plenty adequate, however). Again, a non-issue for me, but still something some people should consider, depending on their child seat situation.
The driver and front passenger seat seatbelts fit ME better in the Sienna. I'm probably the size of 6th grader, so this was important to me.
There were no armrests on the Ody's captain's chairs. Ordinarily, I suppose I could overlook that, but my DS1 and DD didn't like it and since those are seating positions they would be using, I considered their opinion.
I preferred the drive on the Sienna, hands-down. One of the times I test drove the Ody, it was raining. Whether it was the tires or the brakes or both, it handled so poorly, it just didn't sit well with me. The Ody also handled poorly on gravel. The Sienna hugs the road and was a lot smoother. I also got a tighter turn out of it and overall better brake time (in dry weather on normal roads).
I've had mine since March and I've put a little over 8,000 miles on it. I average 22 MPG city. It's been on a 2,000 mile roundtrip road trip and performed like a champ. We were comfortable, no complaints (well, except for the bird that committed suicide on my grill somewhere in Indiana...), and everyone was happy. I even spent a good portion of the ride in the 3rd row entertaining my 2nd row RF'er and I was comfortable.
I know some people say the cabin materials (plastics) appear cheap in the Sienna, but that wasn't something that pinged my radar, much like the fact that the Ody is homely didn't. They just weren't important enough to *me* to make either the pro or the con list.
Both the Ody and the Sienna are IIHS Top Safety Picks for 2011. The Sienna received 3 stars from NHTSA for overall frontal (dinged for female front passenger - I'm assuming chest Gs). I stressed out about that for a little bit and then filed it away under, "For me, I'm OK with that", since I'm usually the only passenger in my vehicle and it's very rare (and when I do, I sit as far back from the airbag as possible). It's more important that I keep my driver and rear passengers safe and, for us, the Sienna does that.
That said, that's why I chose the Sienna for MY family. Nothing can replace the importance of *your* family's needs and/or preferences and the importance of test driving - multiple times, in different weather, on different road types.
ETA: I preferred the transmission in the Sienna as well. As someone who is a firm believer in a standard transmission (and hates driving an automatic), I felt like the Sienna had healthier shifting patterns.