FWIW, my mom HATED the scooter. We had thought that was the best way to go, so we did as ballarinamom mentioned and rented one through Deckers. It was supposed to be waiting for us at GCH, but something went awry and we had to wait for it to show up. When it came, it was extremely difficult for my mom to maneuver and I think it may have been a lemon because none of the other adults could move it smoothly, either. It would lurch and take off at a fast speed no matter what setting it was on. My mom was so stressed by it that after half a day in the parks, she called Deckers and had them come back and take it away. The company was very nice about it and didn't charge, but my mom refused to try another scooter so we got the wheelchair instead. It was so much less stressful than that scooter for both my mom and the rest of us, but as I said, I'm pretty sure our scooter was a lemon. I certainly saw plenty of other people managing to ride around on them with no trouble. The wheelchair was about half the cost of the scooter so it must be less than I said. Do note that it can be heavy going pushing someone in a wheelchair uphill! You don't even realize there
are hills at DLR until you have to push someone in a wheelchair

.
The main reason we wanted a scooter was, as ballarinamom also said, because you can go to and from the hotel and elsewhere outside the parks with it. However, we discovered that we didn't really need to do that and we found (on our last day) that you can add a special thing to your rental that allows you to go outside the parks. We were staying onsite so I'm not sure if you can do that if you're in an off site hotel. BUT...the GCH/CA CMs were SOOOO nice--they let us come and go with the wheelchair through the GCH entrance and into/out of the hotel without making us leave the wheelchair behind and without the special 'license' to do so. There were times when it was easier to leave the chair at the back entrance and walk into the hotel but a few times we did take advantage of just wheeling on through.
I think a lot of it depends on the personality of your grandma! My mom is 77 and has had knee replacement surgery on both knees as well as back surgery with a special thing inserted in her spine, so she certainly OUGHT to use a scooter, but she's feisty, in age denial, and also insecure about driving a scooter so the wheelchair worked much better in our situation.
The nice thing about Deckers is that if you rent a scooter from them and it doesn't work out, there is no problem returning it. They will just come back and pick it up. You can also rent ECVs in the park, but it costs more and you don't get to take them outside the parks.