For the most part, Christmas at the DLR is the same at WDW (decorations, special fireworks and parade, merchandise). The main differences are the attraction overlays and Disneyland doesn't have Christmas parties (yet). I also hear Disneyland decorates more than Magic Kingdom, but I don't know if that's true or not.
Haunted Mansion gets a Nightmare Before Christmas overlay. This isn't a small change, everything in the ride is completely different.
Jack Skellington and Sally do meet and greets:
"it's a small world" also gets a Christmas overlay, but it's essentially the same. The song has some Christmas carols spread in there and there are Christmas decoration outside as well as inside the ride. The change is much less dramatic than Haunted Mansion. I actually prefer the Christmas version of "it's a small world."
There's usually reindeer at Disneyland, but they weren't present last year. Not sure if they're gone for good.
Examples of Christmas decorations at the DLR:
SBC:
Main Street:
Fantasyland (small world Holiday):
Frontierland:
Critter Country:
Toontown:
California Adventure:
Cars Land:
Buena Vista Street:
a bug's land:
Hopefully the photos give you a feel of place around Christmas.