In the book 1984 -- which has far more similarities to today's reality than I am comfortable with -- the Oceanians are utterly and completely convinced that their side is the good side. Throughout the book there are various hints that this is in fact not the case. But the Oceanian government's control on information, combined with people's cognitive dissonance, prevents the truth from being realized. And the few who do realize it are imprisoned, tortured and converted (or killed).
What would today's world be like if China and/or Russia were the dominant power? The answer is that no one knows. No one can know. It's like asking, "what would the world be like if Hitler had won?" That alternate universe was created so long ago that it is simply not possible to conceive of.
It is silly to look at today's China and Russia and conclude that they would continue their current practices and ideologies after becoming dominant world-powers, since said practices and ideologies are very likely what is preventing that from happening. It is also possible that there will be a reversal of roles, with them becoming "good" and the USA becoming a tyrannical, fascist state. I'd say there is a scary amount of indication that the latter is very likely, actually.