Also, to state the obvious, in WWII the alliances were between countries that, for the lack of a better terms, liked each other. And in the case of Western democracies and USSR, there could be no suspicion that USSR would slack off - they were fighting for their dear life.
Now, with climate change, countries that are at best suspicious of each other have to cooperate. It's a truly global problem. So why should I give up my Suburban, when Xi is surely cheating on me and keeps building coal plants? And the other way around, why should I keep living in a cramped apartment w/o AC and commute on a bus, when Americans, Brits, and Germans, who created most of the CO2 currently in atmosphere, enjoy better standards of living?