S.R.
Here is what Consumer Reports has to say on the Oyssey and Sienna for the years you're looking at:
There are 5 ratings, they they classify as "Better" to "Worst", so my 5 are going to be "Excellent," "Good," "Fair," "Poor," and "Bad"
Honda Odyssey 06: Overall got a "Fair" rating.
Honda Odyssey 07: Overall "Fair"
Toyota Sienna AWD 06: Overall "Fair"
Toyota Sienna FWD 06: Overall "Good"
Toyota Sienna AWD 07: Overall "Poor"
Toyota Sienna FWD 07: Overall "Good"
These ratings take into account recorded data regarding necessary repairs on engine repair, engine cooling repair, transmission repair, drive system, fuel system, electrical, climate system, suspension, brakes, paint/trim, body integrity, body hardware, power equipment, and audio system.
And I'll toss out the Chrysler & Dodge minivan ratings, too, just because they're here.
Town & Country 06: Overall "Bad"
Town & Country 07: Overall "Bad"
Caravan 06: Overall "Bad"
Caravan 07: Overall "Bad"
Nissan Quest 06: Overall "Bad"
Nissan Quest 07: Overall "Poor"
If I knew any other minivans off the top of my head, I'd look them up for you, too!