The Model 1935 was used extensively by the Italian military, both as personal purchases by officers, but also as guns issued to specialized troops, couriers, rear echelon soldiers, and Italian aircrews.
It was also used extensively by the German military.
One interesting tidbit about the 1935 (not sure if this is true of the 1934, but I think it is) is that there is no ejector. When the slide is fully to the rear, the tip of the firing pin protrudes through the face of the slide and kicks the empty round out of the action.
Generally these little Berettas are exactly what you'd expect from Beretta -- extremely reliable, robust, easy to operate, and once you get used to the sights and the generally crappy trigger pull and the sights, easy to shoot well.