My knowledge of the wheelchairs is just the general info that I've read about the chairs that are offered at all resorts so I don't know if BC/YC is any different but I would assume that all WDW resorts would be the same. Last I heard, they are manual wheelchairs. You can keep them for the length of your stay if you can get your hands on one in the first place. The word has gotten out about these free wheelchairs so more and more people request them and there aren't a lot of them at each resort. Unfortunately, they really aren't the most comfortable chairs and aren't in the best shape. While they won't be dangerous, they are not necessarily maintained for easy gliding. The intention of them was really to help people out of a jam if they hurt themselves or realized too late that they couldn't handle all the walking and really just until the guest could rent their own.
You'll be MUCH more comfortable if you rent an
ECV from an offsite company. The stickies on the disABILITIES! board has links to several companies that have been used with great success.
ECVs allow the guest in need a lot more independence than a manual wheelchair. In a wheelchair, the guest is forced to look at whatever the person pushing them last points them at. The guest has to go where somebody else decides and look at what somebody else decides. This of generally pretty frustrating for most adults who are used to being pretty independent. With an ECV you are in complete control of where you go and what you do. Also, for the person pushing the wheelchair it is a lot of work plus the person pushing spends much of their time watching the feet of the person in the chair to be sure not to bump anybody rather than being able to look around.
There are situations where an ECV just won't work (ex. if a person has cognitive imparements) but if an ECV is an option then I would definitely recommend renting an ECV or using a manual wheelchair. If an ECV is not an option I would still recommend rending a chair from an offisite company over relying on a resort wheelchair because the rentals tend to be in better condition, are more comfortable and are guaranteed to be there for you.