If you plan on bringing anything into the park. . . ie. a diaper bag, backpack, drinks, snacks, jackets. . .,I would suggest bringing your own stroller. The net on the back of the strollers don't hold very much.
We have an almost 4-y-o DD and will most definitely bring our own for her. It's more difficult folding and unfolding it for the busses, but more convenient for carrying things around in the parks. And keep in mind you can gate-check the stroller at the airport and use it to carry some extra carry-on bags through the airport with you. I find the conveniences of having your own outweigh the inconveniences of transporting it.