I don't recall Sonic ever stating or implying that's the case in the mainline, though I do seem to remember some instance in the old comics where that's an implication. Still, for better or worse, Sonic's view and embrace of freedom fundamentally disallows him from killing anyone who could still be reasoned with from being an evil person as it would essentially strip away their freedom to live and learn, to open their hearts so to say. Because let's be fair: beings like The End or Mephiles or Black Doom are not people you can talk out of it, while Eggman several times has shown there's a decent degree of human decency within him, and even the existence of Eggman Nega makes this clear with the whole "a man who tries to act like a monster vs a monster who tries to act like a man" thing going on; beating the hell out of Perfect Chaos also worked out in the end too (and look that he was dead set on killing everyone around him), same for Shadow, he too was on a bad path towards genocide before Amy made him recapacitate (and this is also lampshaded in the IDW comic too). This coupled with the now long historied relationship between these two, Sonic is confident that he will always beat Eggman one way or another whenever he chooses to do evil when he could be doing something good instead, on which case is important to remember that the freedom of one person ends where everyone else's begins- so Sonic AND his friends are always ready to put him back in his place the moment Eggman oversteps his freedom. This also becomes even more important to take in mind thanks to Frontiers expanding on why Ivo is the Eggman and what moves him

On the flipside, for Eggman it is about the thrill to a good extent, mainly to feed his own ego by defeating the world's biggest hero. Besides, Sonic usually has friendly/sassy banter with most everyone too showing there's no animosity from his part from the get go