I used to be a teacher so we went during Christmas break three times - the week starting on Dec 26th, so the most crowded week of the year. We had a blast! However, crowds were bad. We were able to deal with them quite well though by touring smart. We didn't know about planning ahead in those days, but we knew enough about the attractions to tour smart. BUT - we didn't have kids then. I'd recommend avoiding Christmas week unless your kids are old enough (or young enough, like infants), to go with the flow. Instead, I'd recommend either going during spring break if it falls on a good week, right after school gets out if it's a district that gets out in May, or right before school starts if it's a district that starts at the very end of August or later.
I don't think the Christmas crowds are worth it for a family in most cases. If it's the only time you can go - then yes, of course it's worth it! But otherwise, I'd do a different week. The schools have quite a range of when they go back and that can help the crowds not be crazy at the end of May as well as the end of August.
*We've been in Nov/Dec avoiding the holiday weeks several times. Those are great weeks - but of course, impossible for a teacher in most cases! (I realize there are some teachers who can take off, but I never felt I could since subs in my state are just babysitters so nothing would get done while I was away. I was a high school math teacher, so it was a core class - and one that none of the subs could help the students with at all).