Makes perfect sense, from their personal perspective, which "one thing" was most bothersome/dangerous to them.
A Luftwaffe officer could well be right, that for him, it was the .50BMG. The .50 Browning was our main aircraft armament of WWII. Fighters, bombers, you name it, if it flew, and could physically mount a .50 BMG, it did.
An Infantry officer, on the other hand, could easily have been more impressed by the BAR, carried in numbers by the infantry he opposed. .50s on tanks, trucks, airplanes etc. probably weren't a big a problem in his personal combat history as the BAR gunner and US infantry squad, so his opinion would be different.
It is my opinion that the guns of JM Browning went a long way in aiding our victory. From the 1911A1 to Ma Duece, its tough to find anything even comparable, let alone superior. I'm sure we still would have won, but I believe the cost in blood was lower because we had Browning's fine tools to use.
All else being equal (and it almost never is) bigger bullets tend to work better.