I avoid leaving the water spigot turned on when I'm not around the RV (and likewise turn off the water pump). On the off chance that something starts leaking, I would prefer to be around rather than have many gallons of water flow unattended.
Whether you use city water or tank water to supply your needs is mostly a matter of personal preference. Of course, if you are somewhere that doesn't have a water hookup, the choice is rather obvious: you need to use the fresh water tank to supply your water, or you don't get any. One disadvantage of using the water tank is the noise of the pump.
Per Old-Biscuit's note about the occasional pump running when no water is being used: this does indicate a leak somewhere. Not infrequently, however, the leak is in the check valve built into the pump, and the water is just going back to the fresh water tank and not causing any problems. If that's the case, you can sometimes get it to stop by disassembling and cleaning the pump, or rebuilding it, or often it will just go away on its own when the particle of sand or whatever happens to get washed away. It's certainly also possible that the leak is elsewhere, and hence possibly more worrisome.