I have to confess that I absolutely adore Disney at Christmas; it is truly magical with plenty of extra events. However, if you are going during the peak time when schools are out, it can also be almost miserable with peak crowds. Would you be going then or earlier in December? If so, you won't have near the crowds.
Visiting in September will not offer as many special events and not nearly the same amount of holiday touches, but you will find the Magic Kingdom will be decorated with many fall decorations through Main Street. You will also be able to experience
Mickey's Not So Scary Halloween Party which I actually prefer to Mickey's Very Merry Christmas Party because of the chance to wear costumes as a family, the amazing parade, a chance to trick/treat at WDW, and just the different feel that Halloween brings. You'd also have a chance to enjoy
Epcot's International Food and Wine Festival while the crowds are smaller after Labor Day weekend.
I'm also thinking about the weather difference. September pretty much ensures chances to visit the pools and water parks whereas December could be cold. However, you could risk a small chance of a hurricane in September and may be there when the love bugs are out. Not harmful, but the bugs are everywhere which can make bug-phobic children (or adults like me!) a little on-edge.
So if I had to make a choice, I wouldn't hesitate to recommend visiting in September, but I would prefer a December visit.