Great question! I think that there are a couple of important differences. 1) Whereas "superb" is pretty formal, "super" is almost painfully casual. You'll sometimes encounter "super" in opinion pieces in the newspaper, but when you do, it's almost always because the writer is consciously trying to be informal. 2) Often, though not always, "super" is simply used to emphasize the meaning of the noun or adjective it's modifying. For example, you often hear people say, "I'm super hungry," or "I feel super tired." But nobody ever says, "I feel superb tired" -- that would make no sense. 3) Although "super" often has a strong positive connotation -- the sentence "He did a super job" means something like "He did a great job" -- think of "super" as being closer in meaning to "powerful" or "extreme," and think of "superb" as meaning something like "of the highest quality."

They are synonyms. You can use both. Here in the USA (East coast :) we say more "he is a super guy, a super girl" or as an exclamation "super!" ... Superb would be more used in order to say "That was a superb concert" , "a superb performance", "a superb exhibition" ... "a superb painting/statue" etc...