I think the vast majority of principles translate just fine from one game to another. Where the mechanics are different, they probably shape play differently.
I think CoC is really, really limited both by its history and by horror as a genre. The adventures published for the game over the decades have formed an expectation of play that is ... railroady, IMO. Horror, especially its Lovecraftian branch, is ... plausibly not the best genre of fiction to apply Story Now to, what with the tropes of hidden knowledge and secret histories and tainted bloodlines and insane narrators--it just seems as though the "gotcha" is part of (maybe the heart of) the fiction. In other words, I'm deeply unsruprised you had troubles trying to run it like a PbtA game. While 5E might be limited in similar ways by its history and by WotC's business model (making money by selling published adventures), I haven't found it to be limited in anything like the way it sounds as though you found it to me--horses for courses, probably.