Putin doesn't care in the slightest about public opinion. Being feared and hated by the world is as good as being respected in his book.
Fear is a kind of respect. Not the best kind, but still better than no respect in the realm of international politics. But that fear comes from respect. If Putin comes off as an incompetent schmuck then people will stop fearing him so much. But ruthless and competent is something to fear.
Trump, on the other hand, has the biggest gun in the room in his hands, so even his incompetence is scary.