Follow the theology.
China is growing in “quiet Christianity.” The Communists make a big show about restricting Christian faith to their state worshiping distortion, but in practice they can’t.
With the abolition of communism, the Russian Orthodox church has gained a resurgence; even Putin flaunts a cross, which he wouldn’t have gotten away with in his KGB days.
But the faith in the US is getting lukewarm now. (With a few hot spots remaining, though.)
Communist influence in Russia is not dead, they get second place in most all elections, but usually lose by about 15 percentage points to the Nationalists which is a serious defeat. While not out of the woods, this is good news for Russians, and makes Putin look more genuine when he sides against the Communists and leftists, and with the Church and Nationalists. Putin also has to deal with almost 20% Muslim population in the Federation, anywhere else and they'd run everything.
China, I'm not so sure. The Commies have maintained power and control, although they're far from Commies now. They're oligarchs, and misuse capitalism to get richer, while rigidly controlling showcase Christianity (and everybody else) in the standard commie way.
In my opinion, Russia cares too much about her people to start anything up, and China cares too much about her market. The trouble will come from Western Europe and the Arab states, both will try to use the UN and US as mercenaries to loot those same markets, Eastern Europe, India, South East Asia, and Africa.