Political figures with little real power are almost always more popular than those who do wield real power.

Even the same person can see a big difference depending on the popular perception of their power--see Hillary Clinton's favorability rating after she resigned as Secretary of State vs. now when she is running for President.

If Charles, as king, tries to stick his nose in things, he will be unpopular. But if he remains a distant figurehead, I bet he will still be more popular than the elected politicians in Australia.