Hi Nichole,
December is an amazing time to visit Disney World. There is nothing more magical than the gorgeous holiday decorations throughout the resorts and parks. Plus you will be able to enjoy a number of special holiday events and shows not seen during the other times of the year.
While I can understand the desire to bring the smaller, lighter umbrella stroller, personally I would choose the larger stroller that reclines. You will find the days very long and tiring even for an adult, much less a small child. You and your child will be much happier if he is able to take a nap and relax at times throughout the day, and he will be much more comfortable resting in a stroller that reclines.
You will also find the under stroller storage a huge relief during your trip. I can imagine you will carry a bag with you with a camera, autograph books, snacks, jackets and other miscellaneous items. I can also imagine at some point you may do a little shopping. You will love having the ability to store your purchases and items in the stroller basket and not need to carry them all day.
If you decide you do not want to bring your own stroller on the plane, Disney does rent strollers daily. You may also want to check out
www.orlandostrollerrentals.com who will not only rent you a stroller for your stay, but bring it to you at your resort and pick it up from there after your visit.
Wishing you an amazing time!