It's not only cheaper, it makes each subsequent rental much quicker.
The first time you
rent a stroller, tell them the number of days you want it for. We did it for 7 days, and automatically got a 10% discount. You pay for it all up front. Since I paid for 7 days, I got a strip of 7 paper tickets. They will stamp the date on one of the tickets and give you your rental for that park. When you return it, they will ask if you're coming back later that same day and/or going to another park. If you are, you just go on your merry way. If you're SURE you're done renting for the day, they will take your stamped ticket and refund you one Disney Dollar. You also have the choice of holding on to all your tickets and being reimbursed all at one time on the final stroller return of your trip.
The thing that makes it more convenient: There are 2 stroller lines, one to pay and get your ticket, and the other to present your ticket and get it date stamped and get a stroller. When you rent for the week, you already have all your tickets, so on each subsequent rental you can skip the first line (often a long line) and go right to the fast second line. VERY convenient.
One word of caution: the tickets you get are not personalized in any way, so I imagine if you lose them there is no way to get them replaced other than to buy them again. In my case, rental of a double stroller for 7 days came to $95.20 with the discount. That's an awful big chunk of change to pay a second time if you lose your tickets. Even if I lost my tickets after day 4, I'd still have to pay about $15 a day for each of the remaining 3 days if I still wanted a stroller on those days.
I just returned 2 days ago, it's all still fresh in my mind, so don't hesitate to ask me anything else about this. Enjoy!
-- Eric
