Yes, you can bring your own. The pros of bringing your own would be that you know your child is comfortable in it, and you can use it when walking around your resort or outside of the parks. The cons would be that you have to fold it up to take it on the buses, and there is a slight possibility that it could be taken.
If you take an expensive stroller, you should consider taking a bike lock. You can't attach it to anything because it's a fire hazard, but you can hook 2 wheels together so that it would have to be carried instead of pushed.