Well, he would have been tried by Bolivia, and sentenced to a long, if not life, sentence.
It would definitely affect his image as a tragic "hero", as instead of dying young for the "Revolution", the "Workers" or whatever, he's a dude growing old in some shitty prison.
I'm not sure the US-Cuba relationship would get worse, after all, it would be Bolivia who incarcerated him by some rather serious and real crimes. Cuban-Bolivian relationships would be strained, but there wasn't any love lost between Latin American military dictatorships and Castro anyway, so it's a moot point.
I guess, if he doesn't escape and lives until the end of the Cold War, some Bolivian government might end up pardoning him, and Che Guevara would then be an old man in a world he no longer understands (if he even understood it in the 1960s, that's it)