The pronouns quivis and quilibet both mean "anyone", and utervis and uterlibet both mean "either one". The suffixes -vis and -libet seem to have a pretty similar effect. (I am not sure if there are other pronouns than qui and uter that can take both of these suffixes.) Is there any difference between the two, or are they completely interchangeable?
They're fairly interchangeable. Gildersleeve and Lodge even lump them together. Even in English, the literal translations would also be nigh indistinguishable.
whichever you like
whichever you want
Some grammars will sometimes add little nuances. Smith, for example, says that quivis is more deliberate than quilibet, where the latter has more of a force of "anyone at all, but quivis can mean the same.