The easiest argument for this is in what fans call "Early Sonic Canon," made famous by the comic books and Sonic Bible, in which it is explicitly stated that Sonic and Eggman used to be friends. Back when Eggman was exclusively a scientist for the benefit of mankind, a once brown-colored average hedgehog burrowed into his laboratory. Already being known amongst his friends as the fastest hedgehog, the man who would become Eggman offered to help Sonic by giving him friction-adjusted shoes called Power Sneakers - and it is the testing of this invention that allows Sonic to break the sound barrier. The resulting sonic boom shattered the Kinetic Gyratoscope (the treadmill device used for testing Sonic's new speed), and caused the reaction that made his spikes merge and his hair blue. Granted, this part of canon is outdated and contradicted by Gerald Robotnik's backstory (confirming Eggman's true last name as Robotnik, not as Kintobor as the early canon alleges), so this makes for a less than stable argument in modern reboots of Sonic mythology. However, it is worth noting that Sonic still wears the Power Sneakers after all these years.
But although Eggman's original name serves as a murky counter-argument and contradiction to one sign of the duo's friendship, it serves as a strong implication of another sign: the very fact that Eggman is now called Eggman originates from a nickname Sonic gave him. Whether his original name was Robotnik or Kintobor, Sonic first uses the name Eggman in reference to the scientist in Sonic Adventure. The scientist introduces himself as Dr. Robotnik, to which Sonic replies something to the effect of "He looks more like an Eggman to me." Although the Japanese games have been using Eggman in reference to Robotnik since the original Sonic the Hedgehog, both names were officially canonized and connected with this interaction in Sonic Adventure - and Word of God from Yuji Naka confirms that, canonically speaking, Sonic was the first to give Eggman his current namesake. At this point, this begs a very critical question: Why would someone take the nickname bestowed by an arch enemy, especially a nickname obviously criticizing his overweight body shape, and adopt it as one's own name? Any realistic man who had his entire life ambitions repeatedly shot down by a small animal would likely not take such a thing as nothing more than an affectionate pet name.
Aside from Sonic still wearing Eggman's shoes after all these years, and aside from Eggman using Sonic's pet name after all these years, Sonic's interactions with others makes it arguably apparent that his decision to save the world is often reactionary and personal rather than out of any particular goodness of the heart. Once games started to give Sonic a real voice, he would describe himself more often as "just a guy who loves adventure" (Sonic Adventure 2, to Shadow), or "beating Eggman like it's our job" (Sonic Generations, to past Sonic). Very rarely does he actually make a comment about wanting to save his animal friends; Knuckles and Tails provide far more lines about this. Most of Sonic's character-defining lines come from his taunting of Eggman, or his decision to stop Eggman.
Eggman shows small signs of this same "This is personal" mentality in Generations. When Eggman is trapped in a void between time and space with his past self, one asks the other: "Do we ever win?" When asked to define win, past Eggman immediately replies "by beating Sonic." When present Eggman solemnly replies no, past Eggman makes a comment about getting his teaching degree instead. Past Eggman makes no comment about aspirations of world domination (be it for good or evil intent); as soon as he learns he can't beat Sonic, his entire future just doesn't sound fun anymore.
Much like Megamind and Retroman, Coyote and Road Runner, and Mario and Bowser, Sonic and Eggman contribute to a strange recurring archetype of rivals that never truly destroy each other. Victory is good enough - and from the looks of it, although Sonic is obviously powerful enough to triumph over Eggman again and again, I don't think he has it in his heart to ever land the finishing blow.