I wouldn't buy one for a 6 year old since you would have to buy a higher end stroller if you wanted it to support your child's weight safely. Most cheaper strollers only hold 35 - 40 lbs and even if you wanted to chance the safety issue, it probably wouldn't be very comfy.
The rentals are great for older kids. When we were there over the summer, they were offering a stroller prepaid discount. We knew that we would need the stroller for 5 days so we prepaid and they gave us a ticket for each day. I can't remember the exact discount, it wasn't much, maybe $2 per day cheaper for the double? But, it was convenient not having to wait in the stroller line to pay each day.
I'm not sure if they are still doing the multi-day prepaid stroller discount or not. I did hear rumors that it was going to be discontinued but not sure if that is true.