what's the difference between sucks and bad?

this sucks is a colloquial expression for something that Ты dont like e.g. "this Музыка sucks". Ты wouldnt find it in formal english.
Sometimes they can be used in the same context (this Музыка sucks/this Музыка is bad) but they can also mean something completely different when used differently "she sucked on the nipple"
(yes...classic example)

There isn't really any difference sucks is just considered bad english, but if your talking they both mean the same :)