Amercian design this
[F-22]
Russia copy this
[PAK-FA T-50]
The profound theoretical development in "stealth" technology was done first by Russians (i.e. Petr Ufimtsev).
Moreover, PAK-FA T-50 only visually resembles F-22. And it is mostly due to the physical constrains, operational requirements and future market positioning. It has nothing to do with overall technology. You cannot copy a plane by looking at it. The idea about stealing these technologies is also naive.
By the way, technically speaking Stealth is pretty useless (unless it is cheap enough to have it anyway) as modern anti-aircraft systems clearly see such targets. It seems more like a sale point.
British and French design
[Concorde]
Russia copy this
[Tu-144]
Tu-144 flew first and (again) only visually resembles Concorde. I'm not sure who copycat whom.
Amercian design this
[Shuttle]
Russia copy this
[Buran]
Buran was just a demonstration of technology capabilities. Russians had better, cheaper and more reliable rockets (Soyuz) at the first place which is currently the only pipe-lined technology of delivering humans to space. America is copycatting that at the moment.
Amercian design this
[B-1]
Russia copy this
[Tu-160]
These two aircraft are basically a competition between two designs of a supersonic bomber with variable-sweep wing. Surely Tu-160 was a response to B-1, but similarity is again due to
USA planes will wipe out Russian air force in beyond visual range.
Unfortunately, none of the fighters will be able to come close to each other in any realistic combat situations due to (again) ground/naval-based anti-aircraft systems which are cheaper and have much more superior capabilities against aircrafts.
Even if they are sent against each other, both USA and Russian have air-to-air missiles able to reach targets far beyond visual range.
A little respect to history
I'm trying to counter-balance the widely disseminated point of views due to a large amount of English-speaking sources which naturally follow their own explanations.
I agree that Americans are more powerful than Russians: 3 times richer per person, have 3 times more human resources, warmer client with its economical benefits, reduced threat from neighbors/cultures, multiple historical allies around the world left since the times of British Empire, and so on. But USA never had foreign intervention on their own territory, and they continuously mess with the rest of the world to keep those regions degraded. During WW2 their largest contribution was still economic support rather than their involvement in the warfare which again was largely dictated by the benefits gained after joining the winner's club. These all gives little respect to the US government and their politics.
Russians sustained severe infrastructure destruction, caused most of the damage to Germans, yet were able to rebuild themselves soon after, developing all these things above, sending first human to space, and being able to demonstrate technical superiority in many life applications. Russians are simply not good at business
yet due to their 70-years-long socialistic past. They also do mess here and there but mostly with their own people which I personally find more appropriate.