When we chose our Sienna over the Odyssey the Honda's transmission troubles were making news. It quickly became old news, and my understanding is that there was some upgrade which Honda applied to fix the weak point. It's worth checking to see if there is a difference between years of the same design (1999-2004), or if there is some upgrade service which should have been applied to that particular van.
Web research is good, but it pays to follow the reported problems through to the solution, because everything has some
problems, but most of them can be overcome. Another thing to keep in mind is that a tiny failure rate of a vehicle sold
in such massive quantities can look
like a lot of unhappy owners; it's hard to keep perspective.
As I said, I bought the Toyota, but I think the Honda is a sound choice as well. The two are very comparable in almost every aspect; for instance, my fuel consumption is roughly similar to Per's (with similar 17' widebody 3000 lb trailers).