I know a couple of old-time D&D referees who tried to switch their settings to different game systems (one to GURPS, one to Fantasy Hero), although without reboots. Neither succeeded: a different game system inevitably alters the flavour.
I’ve run the same introductory adventure with different players, but I’ve never built a full campaign from more than one of those runs.
I’ve run Dark Conspiracy in its original system, in a hybrid I built, in GURPS3 and in GURPS4. (I like the setting.) All of those systems are ones in which if you go up against modern firearms without superpowers you are going to get badly hurt or killed, and superpowers aren’t a major part of the setting as I ran it (they came in more later), so while there were some shifts in tone I don’t think they were major ones. Those were different campains with (mostly) different players, though I think we converted the GURPS3 characters to GURPS4.
I have run campaigns in my fantasy setting Jehannum using HindSight (the fantasy branch of ForeSight), Fantasy Hero, and a StoryTeller hack. Once that involved winding up a campaign that had reached the resolution of its issues and starting a new one with a different set of rules in search of a different flavour.
I have run campaigns in my SF setting Flat Black using ForeSight, HERO System, and GURPS 4th, though never wound up one campaign and immediately launched another in a different RPG.
I have several times launched a campaign of e.g. Bushido, Chivalry & Sorcery, or Space 1889, become exasperated with the rules, and translated the characters to ForeSight to continue.