We've done Thanksgiving twice at WDW. My experience is everything is in full swing for Christmas, so no special parades. You'll see a few treats here and there, plus a lot of restaurants will serve a traditional Thanksgiving meal on that day. The American Pavilion at EPCOT and Liberty Square at MK will give more of that holiday vibe than anywhere else just due to the theming. DVC used to get a meal with characters in Thanksgiving costume, but I don't think it's been done in a few years.
As far as which park is best, we did EPCOT one year and it was way more packed than I expected. MK last year was busy, but not nearly as much as I expected. I've heard AK is a solid choice and is probably what I'll do next time.