I've never used Uber, but I have gotten a cab, both from different resorts and from DTD. Sometimes Downtown Disney was cheaper (sorry, Disney Springs) than the resort because it is really close to the church. I have done both. You walk out of the hotel side door, where the DME drop off is, and tell them you want a cab and the CM will hail one for you or call if there is not one waiting in the parking lot. I've never waited long for a cab.