This question comes up here every now and then and my response is always an emphatic BOTH. There are certainly times when an autopilot will work and in which a wind vane is worthless, but the reliability of the wind vane is head and shoulders above the auto-pilots. Add to the fact that that the wind vane needs no power and it the steering method of choice in just about all but low wind/motoring conditions.
I can't remember how many times I've heard of people having to hand steer long distances because their autopilot failed. I've had two failures myself, but don't rely on them as my primary steering mechanism so these personal failures weren't catastrophic. Their unreliably was reinforced yesterday afternoon when an Australian catamaran returned to the harbor here in Pago Pago a couple days after leaving when their autopilot stopped working. They've got another control unit that they tried, but the problem appears to be in the "main brain" of which, unfortunately, there is no spare. They're on a fairly tight time schedule (one of my favorite nautical sayings is that "the most dangerous piece of equipment on a boat is a schedule"), so will be leaving again hand steering to Apia and on to Tonga. At least they've got 3 people on board to share the load.