In general, the SA auto is better for the military, and the DA auto is better for police. This is because, in general, when a soldier points a gun at some one, it is expected he intends to shoot them, while for the police, it is expected that they shoot only as a last resort. And, for that, the DA gun is safer(provided it is in DA mode).
The German military did not adopt the P.38 because of any safety concerns about unintended discharges. They adopted it because they had a huge need for handguns, the P.38 was available, acceptable, and cheaper to make (in terms of cost and manufacturing time) than the P.08 (Luger).
The DA feature was not chosen for any safety reason, it was accepted because it gave a second strike capability to (hopefully) fire a dud round. That was a much higher concern in the latter 1930s than any safety considerations.
All else being equal (and it almost never is) bigger bullets tend to work better.