Everyone agrees that:
Semantically "It's not" and "It isn't" mean the same thing: "It is not".
No doubt here. See: http://answers.yahoo.com/question/index?qid=20110704115859AAmQmxZ
The reason why I'm asking is because Google is suggesting one way regardless the fact the one other one has more hits, see: "that isn't my problem" and "that's not my problem"

In general: which one is more common and what examples where it makes difference come to your mind?