Hmm... I don't think there's a clear-cut answer here. Depends on what your own stroller is like, where you are staying, how you will be getting to the parks...
It's $12/day to rent a stroller. (Not sure if you get a discount for renting two, or if they have a double stroller.) That can add up fast! Disney Visa cardholders get two (I believe?) free stroller rentals a day.
If you're staying at one of the Harbor Blvd or on-property hotels, you'll have to consider the walk to/from the park, since the strollers can't leave the park. Will your child be up to walking... (Or willl you be up to carrying your child?) at the end of a long day? If not, then maybe you want to bring your own stroller.
If you're driving and parking, then you don't really have that concern. You have a different one: you'll have to fold up your stroller to get on the tram to/from the parking lot. If you have a small stroller, this may not be a big deal, but if you have a large one that is a PITA to fold, well, maybe that will annoy you every day and justify the rental.
FWIW, most of my mommy friends bring their own strollers. I have brought my own stroller every time, and I have never had a problem with it getting lost or stolen. Then again, I love my stroller and think it's really easy to push. If you have one of those doubles that is HEAAAAVY, maybe a rental is worth it.