I've been in early October and early December. If you've never been to one, I'd go the other just to have the experience.
September Pros: warmer weather (shorts and tank tops), longer days (before DST), better for pool hopping, and you can get in on the Food & Wine Festival and
MNSSHP (the Halloween party is more fun for me than the Christmas one).
September Cons: it is hurricane season so expect the skies to open up midafternoon or last minute changes. It rained on us a lot in mid to late afternoon, a mini deluge, but then stopped and the sun came off to dry us off pretty quick.
December Pros: less hot and humid (pants and sweater weather), Christmas decorations are awesome, every park celebrates with something special, and you can enjoy the
MVMCP, and since it's in season some attractions usually closed are open (Wonders of Life pavilion).
December Cons: can get downright cold and if it rains you are miserably cold, not great pool weather, days are shorter, takes time away from home preparations.
I prefer warmer weather for my Florida trips and long 2 week stays, so for me September/October is preferable. I also think there's more fun to be had at the Halloween Party what with everyone dressing up and the trick-or-treating throughout the park. It's like a giant costume party with rides. The Christmas party is nice, but beyond the fireworks and parade it loses its appeal. There are only so many hot chocolates and cookies one can eat. However, Osborne Lights are definitely worth several strolls.
Having tried both periods for a couple weeks, my preference is to have a long stay in the Fall and a short fly down stay just to enjoy the holiday trimmings in December. In other words, I'd pick a 4 night studio stay in December, go Christmas shopping, do the party and see the lights but forget trying to pool hop or do many outside rides. I went to the Christmas party twice this last time. First night was cold but clear, second was rainy and miserable. And when it rained, you never warmed up or dried out.
I save my two weekers for September/October. Then I can split my days with pool hopping, park hopping, some early Christmas shopping and I go trick-or-treating for (or with) my nieces and nephews. last year, I brought home a couple bucketfulls of candy, some small Disney bags and made Halloween grab bags for the kids. They loved it so much they are coming with us this year.