Are you in the US? I don't think Previa has been sold here since the 1990's. The Toyota model that's comparable to the Odyssey in the US is the Sienna. My understanding is that the Previa is sold outside the US but if you're here and considering buying one, you may have a harder time on maintenance and repairs because it's not a common vehicle.
Regardless...the Odyssey and Sienna (or Previa depending on where you live) are both great vehicles. I'm partial to Honda because two of my first cars were Accords so I'm familiar with the controls and set up of Honda vehicles. I have a 2005 Odyssey that we bought used in 2011 and have had three years of problem-free driving. My parents have a 2013 Sienna and love it, and it's a very comfortable car for taking their grandchildren places and I've ridden in the middle and back myself and have been pleased with the comfort and room.
Trim depends on what your budget is and what you're willing to pay for. If you can afford luxuries like an entertainment system, sun roof, etc. then go for it. If it breaks you budget, then don't. I think my Odyssey is an EX, which is the mid-level package. I don't have things like a sun roof, heated seats, and a navigation system but it's still a nice vehicle.
Really, they are both such good, dependable, highly-rated vehicles that it comes down to either a random preference (being partial to either Honda or Toyota) or which one you can get a better deal on. Happy shopping!