I've never heard of an auto with a battery, and thought "auto" specifically meant a self-winding watch without one. I'm not a watch guy, though, so what I know about them is a drop in the bucket(or ocean!).
Bought a Seiko SKX007J1 when I was in Airborne School at 19, and after the face got knocked loose ~15yrs later, replaced it with the Black Monster. Had a couple others at one point, that I gave away, but I'm going on 50, and have really only worn two watches in my adult life.
Maybe I should copy/paste that into the "stuff that works" thread!