I know the Germans reissued the 91 series and its derivatives, as well as the svts' and PPsh submachine guns. They also used the captured maxim gpmg and many of the tracked and wheeled vehicles.
I would strongly suspect the Russians did the same as often as possible.
The Sten was developed to use captured stores of 9x19 ammo etc. Many of the British tanks used the Besa machine guns in 7.92x57 as well, though I don't know if that was because of captured stores or not.
The germans also had a regiment of captured russian soldiers fighting for them as well, and issued them the weapons they were familiar with. I was under the impression that's where most of the german stamped and reissued equipment came from.
From a bit of reading recently, it was obvious that some german snipers actually preferred the 91 based snipers over their own.
bearhunter