Superman + DBZ crossover predictions:
If set in DBZ universe:
Bulma finds superman irresistibly attractive in his skin tight spandex, but finds Clark Kent to be a dweeb.
Vegeta finds Clark Kent to be suspicious, and "up to something." Swears the death of Superman, and praises that superman's planet was destroyed.
Gigi hates superman, but likes Clark Kent, and tells Gohan that he needs to study in school so he can grow up to be successful like him.
Goku asks Clark Kent to go with him for martial arts training, which Kent "tactfully" refuses.
Piccolo determines that Clark Kent is actually Superman, but says nothing, feeling it is patently obvious to anyone who pays attention.
Krillan is oblivious to the whole thing, but suspects that Clark Kent must be a powerful fighter after running into him (physically, like through a doorway.)
Gohan's exposure to Clark Kent (and discovery of his being superman) provides the impetus for his later creating the persona of "Super Saya-man"
Lex Luthor shows up as a cameo holding kryptonite, but gets defeated by krillan. This is how the Zfighters discover that Kent is really superman. Prior to this, Master Roshi and Luthor discuss the finer points of Penthouse and Hustler, while Hercule declares himself to be Superman.
I'll let somebody else predict what it would be like in superman's universe.