It depends on each family but here are some things to think about.
If you bring your own stroller you don't have to carry the kids between the car/hotel and the parks. We sometimes rent a stroller but then I end up carrying DS back to the car which is tiring for me. So we usually bring our own. But I do worry a little about someone taking our stroller. It's not a super expensive one but it cost enough that I would be upset if it was taken. Obviously I don't worry about it enough to keep me from bringing it though. Also, and this may make the decision for you, DLR doesn't rent double strollers so if that's what you want, then you would need to bring your own. You could rent 2 strollers though. And if you have a disney visa card you get 2 free stroller rentals a day. Another option people have mentioned is to bring a super cheapy stroller for the walk between car/hotel and the parks and then park it somewhere for the day and rent a stroller to use while you are there since the rentals are nicer than the really cheap umbrella strollers. Hope that helps!