It is important first to note that the truth-value of whether or not Russia Or China would be Better is almost irrelevant, as the argument is Bullshit. We should suspect this immediately by the way the argument is usually forwarded - not "I think American foreign policy is Ok because the alternative is worse" but usually some variation of "oh, you think Russia or China would be better??" - the kind of sarcastic, deeply scandalized and rhetorical format so favored amongst oblivious assholes on most any topic. But in the academic parlance, Harry Frankfurt in On Bullshit defines bullshit:
It is impossible for someone to lie unless he thinks he knows the truth. Producing bullshit requires no such conviction. A person who lies is thereby responding to the truth, and he is to that extent respectful of it. When an honest man speaks, he says only what he believes to be true; and for the liar, it is correspondingly indispensable that he considers his statements to be false. For the bullshitter, however, all these bets are off: he is neither on the side of the true nor on the side of the false. His eye is not on the facts at all, as the eyes of the honest man and of the liar are, except insofar as they may be pertinent to his interest in getting away with what he says. He does not care whether the things he says describes reality correctly. He just picks them out, or makes them up, to suit his purpose.
Where is Russia Or China? It appears on no maps. Russia and China appear on maps, but Russia Or China is non-physical, its geography exists in the realm of archetypes, the Foreign Oppressor. Obviously a world run by Russia would be different than a world run by China: the language spoken, the relative prevalence of Russian food, the proportion of idiots who define themselves as Dogs or Dragons instead of Virgins or Crabs. Russia Or China, by contrast, is nebulous, a place unknown in our experience; it has no culture and no characteristics beyond an opposition to freedom and axiomatically being Worse than America. Or perhaps, reasonably enough, whether Russia Or China is more like Russia or China is immaterial trivia compared to its brutality, its seething hatred of freedom, the environmental impact of its black crusade against the sun, the demographics of its creatures born from wombs of mud and dark sorcery.
To understand this is to understand what we are dealing with. To assert that Russia Or China would be Worse is not a statement of fact, it can't be - We are talking about hypothetical actions of an near-imaginary enemy in a world that does not exist. It is rather a reaffirmation of conventional wisdom, a pledge of fealty to the status quo, and, in its common sarcastic question-form, a demand that the accused do the same or be immediately written off as an idiot and morally incompetent. It usually works, with the accused retreating into "well, no, but...".
A claim that Russia Or China would be Worse (or Better) as supreme hegemon is a claim we cannot not to even attempt to take as a factual statement. Humorously, the people asking this question about Russia Or China generally pretend at being Hard Realists and are either Very Serious People or those who gain inordinate and possibly sexual pleasure from cosplaying as them on the internet. Yet it should be immediately obvious that it is not possible to objectively evaluate even a simple claim predicated on what is "better" - and this is far from a simple claim.
We must define what genre we are working in when we ask about the world as it would be under Russia Or China. Specifically, are we asking for alternate history here, or for science fiction? How and when did they or will they take over? Did Russia conquer Europe? Did the Chinese learn to harness their chi to create incredible energy blasts? Will they take over in the future after irrational leftbros cut our military's daily budget of spoons to the point of making them too depressed to occupy hundreds of military bases in foreign countries? These are important questions for us to ask because they tell us the author's politics and presuppositions. Whether the Soviets finding a crashed UFO naturally leads to world domination, the war of all against all, or peaceful enlightenment is entirely predicated on your politics.
Realistically, we are talking about a Russia (or China) that takes over as supreme hegemon after a major war and/or economic collapse renders America shattered. Even in the best case, this in the short and medium term would be Worse no matter if the actions of the replacement state were completely moral from then on, especially to Americans - the people who tend to make the argument. Otherwise, we are talking about realms of pure fantasy - worlds in which we pretend we used a time machine and went back many decades at least and changed something to put another nation on top, then claim to know definitively how this pretend universe would be.
The material context in which a country exists and gains power is extremely relevant as to how it turns out. A postwar America that becomes dominant through the war economy and the destruction of the rest of the industrialized world develops differently and has different values than an America that becomes supreme through the use of nuclear conquest or Apache magic. I must really stress here that this question about Russia Or China is so meager and underdeveloped, however, that the question of how they come into power is not important. The point is actually to claim that the world under really-existing American hegemony is, if not the best of all possible worlds, at least within shouting distance. Recall Leibniz, the great Platonist, on this topic:
1. God has the idea of infinitely many universes.
2. Only one of these universes can actually exist.
3. God’s choices are subject to the principle of sufficient reason, that is, God has reason to choose one thing or another.
4. God is good.
5. Therefore, the universe that God chose to exist is the best of all possible worlds
Sadly for Leibniz, shortly after expressing this argument his teeth were caved in by Schopenhauer wielding the Platonic form of a sledgehammer, causing him to henceforth have to eat through the Idea of a straw, a form of eating nonetheless vastly superior to our purely mortal chewing. But I digress. This argument can be secularized to describe the position we are engaging. There are infinitely many possible universes, America as it exists only exists in one, this America rules the world, and America is good; so, while there may be other worlds with better Americas, only a world with an America in charge could be the best of all possible worlds.
This seems strange. Some of the ostensible benefits of a sole hyperpower would exist regardless of who was in charge. One benefit claimed is the "Pax Americana," that American dominance gives a safer and more stable world by acting as the sole acceptable initiator of force, patrolling the seas, generally acting as Hobbes' Leviathan. But wouldn't a world under Russian domination also operate under this benefit? It could be said that Russia would be Worse to those under its thumb, but the name of course comes from the Pax Romana. Ancient Rome had a human-rights record generally considered Worse to our modern standards than modern Russia, but still used military force to expedite international shipping and to keep internecine squabbling to a minimum. Isn't that the most important thing?
Of course, we here assume that there is no other choice than some singular actor dominating the world for its own benefit, lest we be dismissed as unserious. A better question is what is it about America that makes it inherently so much better to rule the world than other countries, regardless of how they got there? Why are we more merciful and kind than other options?
Is it our system of democracy, respected by all who participate in it, free of the legalized corruption endemic to lesser states, where votes are meaningful and the process fights to keep fingers off the scales?
Is it our social welfare system, the envy of the world, which provides our most unlucky and impoverished citizens a life of respect and health and happiness, programs supported by the public will regardless of race or creed?
Is it our policy towards immigrants and refugees, people fleeing poverty and horrors almost unimaginable to us? How we comfort them and share our safety and prosperity with a gentle decency?
Is it how we strive to make every worker engaged in useful and productive labor in a safe and dignified environment, or how we strive ever more to make them the decision-makers in their workplaces?
Is it our justice system, which thanks to all of the above boasts the lowest incarceration rate in the world, which has largely abolished institutional racism, and fights with vigilance against its last remnants? How we, regardless of our politics, consider the death penalty a moral savagery?
Is it how we treat animals, how we eat meat only sparingly and how we led the fight for the abolition of the mechanized slaughter-factory?
Is it how our citizenry weeps for the victims of its wars, rare and completely necessary as they are to maintain peace? How we refuse to even possess a nuclear stockpile, let alone use it - god forbid, against a civilian population. How our soldiers are professionals and realize that their lives are less important than those of the civilians in foreign countries they interact with?
Or are all these too broad? In the end, is it the intellect, patience, empathy and decency of our people? In other countries people hit their children, joke about rape in public, believe in demons, rally for executions, cheer for wars, bash gays, support coups, and harbor terrorists. They treat women as second-class citizens, consume trash, pollute, support racist murder.
But not here. Our citizens are svelte and kind and beautiful, and in the end, that's why we must rule.