I had 5 times more geese and 3 times more ducks shot with auto then with pump...
Reasons:
1. You lose sight when reload pump, while you can mantain it with auto, e.g. if you miss, you can keep following the bird, do correction and shoot again instead of getting bird in sights again.
2. Auto is slightly faster and birds do fly fast too
3. Tendency to reload when there is no shells in the mag. In a rush during the hunt, even if I counted shots, I automatically reloaded empty mag... in auto it stays open and you would have a chance to throw an extra shell in the chamber and put one in the mag.
4. Spring. I had it with new Rem 870 Mag. When holding shotgun upwards, the weight of the pump stock moved pump mech. slightly down (just a little), which rendered bold inoperative (not fully locked). Auto has a stronger spring and bolt is always locked. Despite the myths, I had no issues with auto, but as mentioned, pump failed me a couple time.
Good side of the pump:
Clicking sound makes criminals to poop their pants, but auto does it too (however it doesn't look as cool as with pump).