The difference is also that "mu" is a constant clitic (and follows the 2nd position rule) and "jemu" while having the same meaning is never a clitic and therefore is used to emphasise (at the beginning or at the end of a sentence).
The flow of a sentence is the only difference. You would not really say "co jste koupili mu" if you were czech (though everybody would understand) because, well, it is not said that way. At the same time you would only say "Co jste mu koupili" and not "co jste jemu koupili", because it is a mouthfull. Often you can use either and it more or less only depends on where you are from.