The Telluride to Moab trip is all pretty much dirt road. It goes over Last Dollar Pass in the San Juans then traverse's the Uncompahgre Plateau, which is pretty mild, with a final slog up and over the La Sals.
The Durango to Moab Trip is a bit longer, but in my opinion much more satisfying. There are about a 125 miles of alternate single track routes or you can stick to the dirt road. The route takes you over Bolam Pass across Black Mesa then along the Delores River to the La Sals. The hump over The La Sals is through Geyser Pass, so you can either opt for dirt road into Moab or the epic "Whole Enchilada" ride which is Burro Pass to Porcupine Rim.
The really cool part is the hut. It is stocked with all the food you could possibly dream of and they have done an amazing job placing them in drop dead gorgeous spots.