We used to go Thanksgiving week as our "standard" disney trip, until my son entered college. This year we were in Disney from 12/20 through 12/28. I am hopefully completing a trip report soon, but my conclusion on crowds is that it's all a matter of perspective and managing expectations. I went thinking that the crowds would be massive Christmas day and after. Our experience with crowds was typical of Thanksgiving week, and sometimes they seemed a bit lighter, to tell you the truth. HOWEVER, we avoided MK especially on Christmas day and got up early on 12/27 to do the MK rope drop (7 am EMH, and it was COLD!) and we were (literally) the only family actually waiting at the entrance to get in on the left side when the opened the park - there were some families enjoying the train ceremony, and a few families on the other side, I think, but we walked alone down main street on 12/27 at 7 am and rode space mountain 3 times in a row, then buzz 3 times in a row, big thunder 2X (too cold to do more), haunted mansion, peter pan, pirates, jungle cruise, stitch, then went back and used a fp for space mountain (the wait was about 30 minutes by 10 am) and did stitch before calling it a day to go back to the resort, eat "brunch", and take a rest. We enjoyed MK then very much (and it was 2 days after Christmas).
We tried MK on our arrival day on 12/20, but didn't get to the park until about 1 pm. It was quite busy, and the waits for everything were long (except stitch, laugh club, small world). We were able to get a fp for Space with a return time of 11:30 pm. We did return to the park for our 11:30 fp but the parades made it very tough to navigate the park, it was pretty busy, and we didn't stay long. There were extra magic hours at night from 12-3am but I think EMH at night aren't as valuable as morning.
Our experiences at all of the other parks were similar. I don't think the day you go depends nearly as much as what TIME you are willing to get to the park. If you get up early and do the big attractions first the rewards in terms of time saved are huge - then you can either go back to the resort to enjoy the pool while everyone else waits in lines, or you can enjoy street entertainment and smaller attractions. We did, just for the record, sleep in on 12/24 and 12/25 knowing that we'd stay at the parks pretty late those days - Epcot (CP) and Hollywood Studios, respectively.
So.....I'd go at Christmas again (and we probably will) without hesitation. I'd go Thanksgiving. Heck, if anyone wants to give me a trip I'd go anytime! Just know that if it's a busy time you need to get up early. And....I personally don't know a true "non-busy" time at Disney. if you go to WDW any time expecting to just walk on every ride you want to do, you'll be disappointed regardless. If you expect that you'll be enjoying the parks with thousands of your closest friends and plan accordingly, you'll have a great trip!
....now.....I'd best go finish that trip report!