I pretty much agree with got2travel. The parks are extremely crowded at that time. If your enjoyment is going to be affected by having to stand in long lines, you might want to reconsider when you go. If you can deal with the crowds, the decorations are really nicely done, and Disneyland Resort is beautiful at that time of year. However, do not expect to go on a lot of attractions, even with Fastpass from Dec 27-31. March is bound to have lighter crowds - but, you may run into rainy weather (you might also get that in December, too). I think last March was very rainy.
December - big crowds - but long hours, and more shows, parades, etc.
March - smaller crowds - but shorter hours, less shows, parades, etc.
My opinion -- Get a multi-day hopper, Pick a couple of days during the week - maybe 27-29 to spend more time in the parks -- use your time to watch shows, enjoy some attractions (pick a few that you want to visit each day), and enjoy the other fun stuff - cookie decorating, Christmas caroling, etc. Go to Knotts Merry Farm on another day, and break up your days at Disneyland by relaxing at the hotel, too. Be sure to go on It's a Small World Holiday & Haunted Mansion in the morning (get fastpasses) because their lines are impossible at night.
After 1st of January go back to Disneyland to enjoy the attractions you missed, and do other fun stuff.
I think that's what I would do with my family.