When we went in 2005 we brought our full size stroller with us. My DD was just shy of two years old (actually she was 23 months old). It was perfect for her (reclined, had a snack tray, and an awning). We wound up taking the snack tracy off and leaving it in the resort room. She was able to walk, run, etc with her older siblings but when we had to move from one side of the park to the other side, she was able to sit back and relax. Additionally, she took a nap EVERY single day. DH would take the older two on a ride and I would take the little one to a quiet, boring, corner and just walk back and forth. Then we had two hours of bliss. Furthermore, the full basket on the bottom and the drink holders for the adults was quite nice.
This year, DD will be two months shy of five years old (both of her siblings are teenagers now). We are bringing the big stroller again. No, I don't expect her to use it much. The basket will be wonderful, she will have a chance to sit and rest for a minute when she needs too, and she will be able to sit in the stroller when we have to move from one side to the other. Lastly, at the end of the night, when the little one is exhausted - it will be nice to recline the seat and let her relax.
Essentially - it's her safe haven.
But, that's just my two cents.
OH - and lastly - it's wonderful to put her in when moving through the airport. We just gate check it from there.