My suggestion: drive all of them first. When we were in the market for a minivan we drove the Sienna, Odyssey, Sedona and Chrysler T&C. We didn't drive the Quest simply because neither my wife or I could get over the funky styling. Here is how we broke it down:
#4 Sedona: Excellent value, but it is ANCIENT. It honestly suprises me that they are selling enough of these to keep them around. You can buy a Mopar for a tad more, so this way excluded.
#3 Sienna: I really wanted to like this van. We rented one with 7k for a road trip to Jersey and I hated it more and more with every mile we drove. The interior might be improved over previous generations, but it is still super cheap feeling. Rattles and squeaks galore. The ergonomics and layout of the dash seemed like an afterthought. The standard sound system was tinny - like a Japanese car from the 80s. The seats got uncomfortable as the miles dragged on. It did have a ton of power, but delivery wasn't linear enough for my tastes. Got 24 mpg on the highway with just two of us and our suitcases. Like I said, I wanted to like the Sienna, but everything about it seemed like an afterthought except the drivetrain.
#2 T&C: This was the biggest surprise on the list. I actually really liked the T&C when I thought I wouldn't. Mind you, this was one of the refreshed models (I think 2011 and up?) and it was great. Better interior than the Sienna: much better ergonomics, no squeaks/rattles, high quality materials where it counts, good sound isolation and more versatile seating. The interior is the high point of the van. The negatives were the aging styling, very touchy throttle (peeled out more than once, it is very aggressive at tip-in), mediocre fuel economy and questionable reliability. The vans made prior to the refresh were riddled with fit/finish and electrical issues. Perhaps those issues were ironed out the the refresh, but I couldn't get past it.
#1 Odyssey: As you can see from my signature, we went with the Odyssey. We bought it in August 2013 as a 2014 model and we were still able to get it for invoice with some haggling and dealership shopping. This made the price VERY competitive with the T&C. Before everyone starts freaking out about VCM and transmissions, let me make the case for this van.
Engine/Economy:
The Honda 3.5l V6 strikes the best balance in the segment. More than enough power than the sluggish Sedona and better/smoother delivery than the Sienna and T&C. The VCM is, for the most part, seamless and really does give better MPGs. We haven't gotten below 21 mpg with all city driving and have got 26 mpg highway (should get better past break-in). Yes, there have been issues with VCM. However, my research has shown that these are more common when owners use cheap oil/long OCIs, do ALL highway driving, or have the very first VCM models. There are plenty of VCM Odysseys/Pilots/Ridgelines with 150-200k with no issues. I am OCD about my maintenance, so this was a non-issue for me.
Transmission:
Lets address the boogey man in the room, the transmission. The 5 speeds in the 2011 models forward were completely reworked to avoid the previous issues. For 2014 the 6 speed manual was made standard across much of the line. This transmission has proven tough and was built with the weight of the vehicle in mind. Honda's automatics have never done well with neglect, but again I'm OCD about that so it was a non-issue like the VCM. I feel comfortable that it will be fine for the long term.
Styling:
The 2011+ Odyssey's are, IMO, the best looking minivan on the market today. The Sedona and Sienna look like blobs, the Quest looks like a Japanese moon orbiter and the T&C looks like a box. The Ody is sleek, chiseled and modern without looking over the top.
Interior:
Best in class interior, although the T&C came close. Fit and finish is excellent, soft touch plastic and chrome in all the right places, smart seating options and storage, and the ergonomics are good (the 2011-2013 models were more button heavy, though). The seats are firm but very comfortable. Low interior noise helped by ANC tech and I've been in several of these and they have NO rattles or creaks that I have heard.
Suspension and Handling:
This is a firmer vehicle than most in the class. I like it, but some may not. I think that it helps improve the feel of maneuverability. However, it won't jolt you unless you hit a massive pothole. Handling is solid for its size and the steering is direct and linear. Ridiculously small turning radius.
Anyways, I could go on, but both my wife and I are extremely happy with it 6.5k on the odo. I don't think you could go wrong with a 2011-2013 Ody, although I would see what kind of deal you could get on a '14. You may have different priorities than us, but it is worth looking at as it is a large purchase and you need to be happy with more than JUST reliability to keep it long term.