I think one gains the following with an auto:
More practical reliability: Autos are less prone to user error. People who shoot much three gun will tell you they see many more user induced malfunctions with pump guns than they do with auto loaders. And these are shooters that probably shoot more than the average Joe. I know, I know, you never would short stroke your pump or anything like that.
Good autos are very reliable, particularly with loads suited for defensive use. My 930 SPX has never had a failure in several hundred rounds. My main S12 (others I haven't shot much) has also proven its self highly reliable as well. Both are much less prone to user error than my pump guns.
Followups: Shot timers don't lie and I am faster with my autos than I am with a pump. This is particularly true shooting slugs and buck.
Recoil: Every auto loader I own is softer shooting than any of my pump guns.
Firing/operation from improvised/unconventional firing positions: When one starts moving and shooting from different positions an auto loader is simply easier to use. This is its own point but also relates back to my first one as well.