Actually Prigozhin is arguably waaayyyy worse. Putin is a ruthless warlord just like Prigozhin, yes. They have equally virulent ideologies, yep.
But Putin is a politician first and Prigozhin is 100% not. Say what you want of Putin but deep down he still gives a shit about projecting certain images of control, law, etc -- he still values the opinion of certain international communities. He is still the leader of a government, not just a battalion or an army.
Prigozhin doesn't give a shit about any of that, he is a simple and ruthless warlord without any pretense of governance at all, who only understands force and who has no qualms about being open in his toxic ideologies.
I think it's extraordinarily unlikely Prigozhin actually accomplishes any of his own goals towards Russia because he isn't a politician and he's just a thug, but I also think it's equally unlikely Putin's Russia recovers from this. Wagner was Putin's pitbull. They were virtually the entirety of professional real soldiers Russia had under its command. No more pit bull changes things dramatically. We can easily expect a social "downgrade" of Russia's status as superpower in the eyes of other nations. That leaves some big doors open for China, India, Pakistan, Iran, Afghanistan, and of course, the United States.
We may be on the cusp of a second break up of the USSR, further breaking Russia down into disparate nationstates. That possibility offers a lot of problems on its own. It's no longer a question of "rogue warlord gains control of russian nukes", now its "russian nukes don't exist, now those nukes belong to 15 new whatever-istan nations, each without any pre-existing relationships or treaties". That's scarier. Doubly so because in that big muck of former Russian states, Wagner could still be around in the middle of it with the biggest dick on the block. He'd predictably go Atilla, march through every one of them and conscript every dude over 16 to fight. And history tells us over and over just how those situations end: global-scale wars. Conqueror types never stop, they just keep conquering until they get stopped.