We were there last year, December 21-30 and it was amazing - our best trip ever!
7am EMH at MK are your best friend! We hit those a few times and got so much done. The park was pretty empty for the first couple hours. By 10-11am we were headed out as the masses filed in. We had park hoppers, so spent evenings in a different park.
We did venture over to MK one evening to see it all lit up and have dinner at BOG. The crowd was pretty thick and not a lot of fun to maneuver around. We had dinner, did our fast passes and left. So, I can understand if people always arrive later in the day to MK, they might find it miserable.
We did not find crowds in the other parks to be an issue at all. We were able to score same day FP's, rearrange dining last minute, and had no issues with WDW transportation.
It took planning, but our experience was certainly not the nightmare I have read about on these boards. I think it helped that we had 10 days to get things done. If you're trying to do a 4-5 day trip over Christmas, it's going to be harder.
Spending Christmas Eve and day in WDW was so magical. The only thing keeping me from doing it every year is that hotel prices are so high.