I never see Axis taking .50 cals and maxiums left on the field, but I always see them taking back there MG42s and 34s. I wonder why...
Well, Ostheer it is more difficult if we're talking about right after battle since they will lose the squad if it's only three men and they only have 4 man squads. I've see plenty of OKW stealing weapon including maxims/50cals with their Volks while Osttruppen tend to steal any weapon they can find.
Soviets will grab anything since they make any support weapon six men which makes decrewing stolen 42s ridiculous and US grabs things just to keep them out of Axis hands.
Also because the support weapon share this weird thing. Allies want MGs that can hold ground, Axis want MGs to respond to flanks. (late-game this is not as vital)