One of the benefits I hear most frequently mentioned is being able to simply shut off the app any time they like (while not actively carrying a passenger, of course). Drivers, in other words, have complete control over their working hours. In addition, drivers, not Uber/Lyft choose where to work: They can hang around the airport, downtown, or out in the suburbs.
Drivers are also not penalized for refusing individual fares--only for refusing greater than some threshold fraction of fares offered. Uber. Uber and Lyft do not prescribe the route a driver must follow, either. The app does offer a suggested route (which is not usually the best on Uber--maps in their driver app are notoriously poor), but the driver and passenger have the flexibility to use a different one.
This is how it works in practice, and frankly it seems to me that they are bona-fide contractors.