Personally we preferred renting the during our last 2 visits to WDW. If you purchase a "length of stay" rental, you will receive a discount(we pd about $8/day with 7-day length of stay for single vs $10 if you rented daily) and once you pay the 1st time, you walk to the front of the line to get your rental pass stamped and pick up your stroller with little or no wait.
Although different parks have different strollers, we also liked the idea of using it to hang our snack backpack and a place to store the extra sweatshirt/jacket/towel/poncho, etc that you may need(depending on what time of year you go, of course). My kids are 5 and 8, and we even paid the extra for a double one day when we knew we would be at MK all day and sure enough, the 8 yr old was crawling in for rides as the day went on and even watched the fireworks snuggling next to his sister(she was not too enthused about it but she learned to adjust!!)
Also, as an aside to Noahynav, you can check with your airline regarding their baggage policy on checked strollers. In the past we used our stroller right up to the gate, then asked to have it checked there(they will get it on the plane and if you request should have it waiting for you at your next gate).
Finally, as many people have pointed out, WDW CM's are notorious for rearranging strollers parked outside a ride/attraction/show or even some restaurants(case in point, Kilimanjaro Safaris at AK)...so you want to do something to your stroller to make it stand out from the others. Some suggest tying a bright piece of material around the handle or attaching the cheap snap glow sticks to locate it easily at night. Even if you bring one from home, or pick one up at Wal-mart on 192 before you get there, there might be many others that look just like yours...
Just some thoughts from one who has done both the hauling from home and renting from the parks.