For the carsharing member (driver or renter in p2p terms), some adjustments will be necessary — it seems likely that in most cases instead of knowing a couple of favorite vehicle locations near your home or office, you'll have to go on the internet (or ideally smart phone) to locate the cars that are available during the timer period you have in mind; and there may be a little anxiety finding the location the first time, particularly in cities.
For the carsharing company it transforms a major expense (leasing or owning the fleet) into a variable cost that they only pay when the car is actually making money. And, the lower cost structure means that carsharing can be feasible in less dense, more suburban locations (i.e. lower hours per day utilization), increasing the benefits of carsharing beyond the center city and close-in neighborhoods of the relatively few cities in the US that presently have carsharing. That's the heart of why I think is peer to peer a next big thing.
A side benefit of p2p is that, in the same way that using carsharing instead of owning a car (or 2) can be a transition to car-lite lifestyle, renting a car out to others may also serve as a transition to a car-lite lifestyle for vehicle owners.

