I have an ST6001 and it is the best, most reliable piece of kit on my boat. It steers a course under sail, under power, to a course or to the wind. There are two things about AP's that are important to remember.
The first is that they tend, depending on the gain and sensitivity settings, to correct more than necessary when first engaged. But then they start to "learn" repetitive adjustments and begin to ignore them. The frequency of adjustment on a long voyage goes down to such an extent that on a Pacific crossing, I used to often wonder whether it was still working because the wheel wouldn't move for minutes at a time and then almost imperceptibly.
Why is this matter important? Because often people are critical of the holding capacity of the AP immediately after it has been engaged but they all do that for a while. Also the perception that they eat up power is erroneous on a longer voyage because with the adjustments becoming so small and infrequent, the AP uses very little electricity.
The second is as SD has already said, the wind vane setting needs time to settle and will not successfully adjust to the frequent wind shifts caused by buildings, hills and so on. But once at sea away from the influences of land, the boat will hold a relative course to the wind unerringly. We sailed a course to the wind on a 45nm trip across open water and the AP held the course with absolute precision. I do not believe that a skilled helmsman could have done it better.
There was one question above about how many members have actually got wind vanes on their boats. Well, the Raymarine
and I suspect most other AP's will interface with the NMEA signal coming from the standard wind instrument and don't need a dedicated vane. The down side to that is that with a high degree of heel the wind vane at the mast-head provides a reading that may not be as accurate as one would wish for. However, for long distance cruising where most of the sailing is done off the wind, this is of little concern.
These are just my own observations, YMMV. One thing I will say with absolute certainty, I will not go on a long trip without my AP working. Imagine a crew member who never sleeps, never needs lunch breaks, never goes to the head, never gets tired? That's your AP.