With my interests and my line of work, I often hear the old Russian copy story. To a large degree, it's an urban myth. Many of the aircraft and engines referred to are actually license build arrangements, and in typical Russian fashion, the originals were improved on.
I think it all started with the Russian use of the Rolls Royce Nene in the MiG-15 prototypes. Britain was hoping for a license deal, but the Russians reverse engineered the RR engines that they had bought, and operated them in different variants in production models. Russia was well on the way to being a leader in aerospace before the war broke out, but that put a lot of research and development on hold to concentrate on the war effort. After the war, Stalin was acutely aware that the West was making advances in jet technology, so a quick catch up plan was hatched. The main thing they realized was that it's a waste of time trying to re-invent the wheel, so 'borrowed ' technology was used to a degree. The copy myth grew from there.
The Russians never copied anything because they were lazy or stupid- it was always for political and technical expediency. If one was to list their firsts in aerospace design and achievements, it would use up a lot of paper.
One example is that the Russians in 1957, pioneered, developed and produced a pressure demand oxygen mask pressure compensating system. The Americans may not have copied it, but it took them an extra 35 years to produce what they call the Combat Edge System for the F-16 and F-15. The Russians had it when FE Holdens were rolling off the showroom floor.
All in all, I'd estimate the copying to be about even on both sides.