To answer this question as fairly and accurately as it's possible to answer a speculative question, to determine which of the two sides would have been victorious would require that we outline parameters for what would constitute a victory. For example, without knowing which side struck first, it would be...
Best answer: To answer this question as fairly and accurately as it's possible to answer a speculative question, to determine which of the two sides would have been victorious would require that we outline parameters for what would constitute a victory. For example, without knowing which side struck first, it would be difficult to map out a very clear objective for each side.
Had the Soviets foolishly decided to attempt to overrun Western Europe and had the United States and the United Kingdom attempted to stop them and drive them back, then an American and British victory would have been inevitable. Obviously it would have been a conflict of the first order and in some instances the extent and ferocity of the fighting might have even exceeded the fighting in the war that preceded it, but the plain and simple fact is that the Soviets would never have been able to hold on to their gains against the combined forces of the Americans and the British dominions.
The Soviets had been victorious in the East for three reasons: because they were willing to pour an endless stream of men at any problem and that the continual human wave was something that the enemy could not overcome, because the German High Command had made some very, very poor strategic and tactical decisions which made a German victory an impossibility after a certain stage of the fighting, and lastly because the other Allies kept the Soviets afloat. That is the long and the short of it.
After losing tens of millions of people, seeing their cities levelled, the countryside ravaged, after food supplies had dwindled, the Soviets were in no position to prosecute a full-on aggressive war. Yes, they had a massive amount of troops, tanks and artillery in Germany and Austria, but the further they attempted to move from their own supply lines, the more difficult it would have been for them to move further west. And even if their initial strategy had been to simply dig in and wait until they were able to consolidate their forces a bit better, it's not as though the Americans and the British wouldn't have noticed.
In fact, as desperate times call for desperate measures, it's likely that the Americans and the British would have considered re-arming the Germans and having them join in on the attack on the Soviets. The Germans would be fighting for their homeland against Soviet occupiers who were notorious for their brutality against the German civilian population. The Germans would have fought like wild animals ans the Soviets never would have made it to the French border.
Again, and all of this is not to mention that the United States and Britain were capable of constructing atomic weapons while the Soviets were not. It's very unlikely that the Soviets would have been compelled to continue the fight had the Americans and the British decided to drop atomic bombs on Moscow and Leningrad. End of story.
Now, to be fair, it might have equally been a case of the Americans and the British adopting the opinion that the Soviets had grown far too powerful and posed far too great of a threat to their interests and decided to attack first, but that decision would have proved to be quite costly, even if the end result were to be the same. Firstly, the United States and Britain don't work in the same manner that the USSR did. In the United States and the United Kingdom, public opinion is a very big determining factor in what actions the country takes or does not take. After six long years of war, it's almost a given that most Americans and Britons, not to mention Canadians and Australians, New Zealanders, French, Poles, etc., would have been completely exhausted and would not have been keen to embark on a fresh military campaign that had the potential to rage for an equal number of years.
To destroy the Soviet's power base would have required an assault similar to the one the Germans envisioned and failed to execute. Instead of besieging cities and terrorising the civilian population, the Americans and the British would have known that destroying the Soviet Union's ability to prosecute a war would have been the only way to achieve victory. And how to do that? Well, to be honest, it would have been nearly impossible. But the primary goal would have been to eliminate the Soviet Union's industrial capacity. That would have required American and British bombers to push deep into Soviet territory. And like what had happened before, the Soviets would have moved their factories farther and farther out into the deep hinterland of their vast territory. They would have been constructing aircraft and tanks, bullets and bombs, mortars and uniforms and helmets and everything else they needed in caves out past the Urals or would have constructed brand new factories and laid rail lines leading into them way out in the wilds of Siberia. It would have been a nightmare.
Which is where China probably would have come in. The Americans could never have trusted the Japanese to join the fight on their side and US public opinion never would have swayed in that direction. But the untapped millions upon millions in China would have been an ideal addition. Not to mention that the Chinese probably would have jumped at the chance to expand into vast portions of practically uninhabited Siberia, so the incentive for them to assist would have been massive.
Would it have been a devastatingly horrific conflict? Yes, absolutely. But no matter which angle you choose to approach the situation, it's an inevitable American/British victory, no way around that.