China and Russia already have more oppressive systems in place which would be able to exercise a greater level of control, but they are also dependent on a lot of infrastructure, like for the internet, that is based in the West and would be easily cut off in a tense situation.
There are enough resources in Siberia and Southeast Asia, which would likely fall under Chinese control, as well as Africa, which has a growing Chinese influence, to make for a very prolonged conflict. It is likely that Africa would be a major battleground of this csituation / conflict due to the the incidence of rare earths there. Most of the materials used in the electronics we are addicted to are made in China or Africa, and China would be fairly well insulated from any kind of a direct attack due to the ease of deploying defense systems from Russia through the Siberian plains, so NATO would likely oppose by trying to attack the markets that are the lifeblood of the Chinese economy and limits their access. This would give rise to a restoration in American manufacturing as the economic war heated up.
If you want to understand the power, follow the money- while Western backed institutions like the IMF and Bank for International Settlements may be active in the formation of policy in places like Brazil and and India, the new BRICS development bank sponsored by Russia and China will assuredly try to supplant the IMF wherever it can, forming a globalization of resistance to the current dominant schools. Anti American sentiment in South America is also very high due to decades of the US and CIA backing brutal and unpopular dictators there, so you could easily see a bloc of Brazil, Bolivia, Venezuela, and possibly other states forming against American aligned Colombia, Ecuador, and Panama.
You have intelligent and rational players making the decisions here- Putin’s popularity is at an all time high because Russians feel the pride of imperial glory returning, however, nobody is going to take any unnecessary risks. It is a simple question of what can be gained. I heard someone once say that in Chinese the word for “crisis” and “opportunity” are the same word.
In Western Asia Russia sees an opportunity to expand its influence through an emerging shiite bloc composed of Iran, Iraq, and Syria, putting pressure on US backed Saudi Arabia by backing Shia in Yemen. This gambit is likely to fail in the long run because of the preponderance of Sunnis in the region, but they can be used simultaneously to secure a presence in the Eastern Mediterranean and to block access for Qatari gas to the large and lucrative European market which is currently the lifeblood of the Russian economy, and would be threatened by a consolidation of NATO power in Western Asia. In other words, all Russia really has to do in order to win in West Asia is to not lose. This means a stalemate is actually a desirable outcome, and the present offensive in Aleppo is likely more defensive then genuinely aimed at retaking territory. It would honestly be very hard to estimate who will win this war since there are many factors that cannot be calculated, but I think it is safe to say it will not be like World War 2 where you had a decisive victory in a few short years, but it is rather more likely to be like the wars of the middle ages that spanned generations. I would expect it to last at least three generations, and by the time something resembling "victory" is finally obtained, the political landscape will probably have changed so much that the winner may not even be recognizable to us.
Of course, looking at history is the best way to determine the future, and we can see that fortunes have been fluctuating between West and East, with Roman and Persian empires going at it for centuries. The last few centuries have been characterized by dominance of the inheritors of the western Roman empire, now known as NATO, due to a surge of resources resulting from the conquest of the Americas.