It totally depends on your point of view and circumstances.
Rentals, imo, are completely inappropriate for children 2 and under. They are not comfortable for napping. The price of renting everyday can add up, especially for 12 days--even with a 10% multiday discount. You won't have one at the resort, DtD, airports, walking through the parking lots, etc. It's a hassle to wait in line to get them and return them, and must be repeated if you hop parks or leave for a restbreak. They all look alike. Of course, you can always rent from a baby rental supply rental place. Lots of children feel more comfortable in the stroller they know. It's easier to deal with the stroller you know as a parent. You know how clean your stroller is.
Bringing your own though could be hassle on the bus (Although I've, personally, never found it to be despite the stroller size) or other WDW transportation. If you have older children it could simply be easier to just get it when needed, if needed. Buying a stroller just for the trip could cost as much or more $$$. Unused days on a multi-day rental will be refunded. One less thing to haul around the airport, or pack up in the car.
That being said, we bring our own. No point on spending more money that could go to something else. And when our boys were clonked out in it at the end of the night, it was the best advertisement to bring your own. Pushed them around the park asleep, rolled them on the boat asleep, pushed them through the resort asleep and put them in bed without ever disturbing them. No having to carry them (especially with a 4yo the size of the average 6yo), no whining. I love the convience, and ease.