The US
Under the initial question,this would go back to 1948. If we look strictly at Olympic victories,the US has a clear lead,with Cuba and Russia close behind,and even then it gets skewed because many of the Russian victories are under the old USSR,which counts neighboring areas that are no longer considered Russia,and Cuban fighters rarely have pro careers, so the international games ARE their Pro career.
If you extrapolate those numbers to pro careers(and except for the former USSR and Cuba,that would translate normally) most Olympians end up with one title or another,so the US would still be in the lead.