Bob P said:
Towncar service is usually a lot faster, and offers the flexibility of a grocery stop. Of course, it is not free, and you do have to collect your own bags from the baggage claim area.
I don't agree that a "Towncar service is usually a lot faster." A towncar service can be faster. DME can be faster. If a towncar has an edge, it's a small edge.
Both options require some waiting at the airport. With a towncar service, you need wait for your luggage at baggage claim; then you wait for the driver to retrieve the sedan from parking. With DME, you wait to check in; then you wait to board the motorcoach and for the motorcoach to be dispatched.
If your timing with DME is good, you could be on the road while other passengers on your flight are still waiting at baggage claim. Disney does a good job dispatching motorcoaches based on actual need, rather than on a rigid schedule. But there's also the possibility that you just missed a motorcoach to your resort, as well as the possibility that your motorcoach could stop at one or two other resorts before your resort (or supposedly at three other resorts, although this seems very rare).
The big advantages of a towncar are personal service, timing that does not have to take other guests into consideration, the option of a grocery stop, and a nonstop ride from the airport to your resort (except for the optional grocery stop).
The big advantages of DME are the luggage service (you check your luggage at your home airport and it "magically" appears in your room a few hours after you check in), comfortable seating regardless of the number of people in your party and, of course, that's it free.
As an alternative to grocery stop, there are grocery delivery services such as GardenGrocer, WeGoShop, and Goodings.
Also, see this recent thread on the same subject:
ME bus or towncar?