Both would be fun, however we did your option one last year and really liked it.
Why?
-less crowds before Christmas Day. Now the parks are already pretty crowded right before Christmas, but I couldn't believe how much MORE packed they became starting Christmas Eve. I was glad we were able to get on loads of rides before the packed crowds crowds came in!!!!
Now I guess since you would stay past New Year's the crowds would thin out then, however we seem to go more full tilt on the beginning part of our trip and then relax a little more toward the end so I wouldn't want to depend on that time after New Year's to get lots of riding in.
-Also not sure if you have kids, but they just adored being in Disney for Christmas!! We brought a small 4 ft tree, lights for the balcony and decorations. The kids loved it! And since we were going to be there for Christmas we didn't put up a tree at home and just went real light with the decorations which was a wonderful bonus when we got home as there wasn't alot of pack away as far as decorations!! If we hadn't arrived until the 26th my kids would have demanded a tree for Santa!! And yes Santa still found on, we wrote him a note and he delivered right to the BLT!!!
-We all loved it so much being there over Christmas that we are already planning to be there for Christmas 2013!!