Hi Anna,
With your son being older, this is a bit trickier to answer. My first thoughts are that your own stroller is always the best because you will have it at the airport, the resort, and to/from the park. Renting a stroller is only good for inside the parks; there is a lot of walking that happens beyond the parks. And when your child falls asleep on the bus ride home, having that stroller to bring him back to the room is a huge benefit. However, you will need to fold up the stroller on the bus, which can be cumbersome to manage.
With that said, by the time my sons were in grade school, they began to not use a stroller at the parks. So if you bring your stroller along, you may find that you are carrying it more than your son may be using it. However, I know every child is different, so your son may feel more comfortable and relaxed by using a stroller. If you are unsure, you should know you can rent a stroller if you need one later - especially in the evening or at Epcot (which can tire out little ones quickly with its size). If you click
here, you can find the information about stroller rental at WDW.
And of course, you could bring it along with you to have it
just in case, even if it never leaves the rooms.
Have a wonderful trip!
Kara