I think the difference is that one has quantifiable power and one doesn't. A work of art can sway the public's opinion of a political figure, but it doesn't have the authority to directly take the politician out of power. In a lot of the world, political figures can censor and shut down art that they disagree with.
I'm assuming you're from Australia because of the Australian news link, but here in the States, Presidential Candidate Donald Trump (who has hosted Saturday Night Live twice) wants the show canceled now because of his impersonation on the show.