What a band 8.0 answer sounds like
I'd say governments carry the greater responsibility, though individuals certainly can't be let off the hook. The reason is scale: a person who recycles diligently makes a small difference, whereas a single policy, say on emissions from power stations, can shift millions of tonnes of pollution at once.
That said, I don't think the two are really separable. Governments tend to act when voters demand it, so personal choices, such as how we travel or what we buy, send a signal that politicians and companies eventually respond to. In my own country, for instance, public pressure was what finally led to the ban on single-use plastic bags. So I'd say the most effective approach is for governments to set the rules, and for citizens to keep the pressure on.