The first difference between the two is that they are of different standards. The major difference, however, is in the direction of current in the two systems between the dimmers and the driver. 0-10V is a current source system, and this translates to power ranging from 0-10V signals which means you need a mains connection.
1-10V, on the other hand, is a current sink system. In this case, your dimmer will not need a mains connection. It is important, however, to have a mains switch in case you need to switch off the light.