Putin is a sensible moderate by Russian political standards, which makes him a raging right-wing nationalist by European standards, because of how heavily Europe leans to the left, and a bad guy by American standards, because he's considered a threat.
The KGB were always the pragmatic, coldly calculated, nationalist-wing of the Communist party, purely concerned with furthering the interests of the state (and by extension the nation), in practise the followers of Stalinism, rather than Marxism, and that is where Putin draws his inspiration from. While he might have an ideological foundation of his own, he is willing to compromise when it is in the best interests of the state (and obviously himself).
Problem with Xi, is that he steps all over the idea of individual freedom, which might appeal to the collectivist Sieg Heil-types (which in reality are a minority of trolls/disturbed individuals), but not necessarily Western-minded individualists. He'll crack down on Islam, sure, but he is also cracking down on Chinese cultural tradition. He wishes to extend surveillance over everybody. That's not someone that is easy to rally behind, except when observed at a distance.
Even with Putin being ex-KGB, he is really not that interested in people's personal lives, and how they choose to live them.