They are both correct in normal speech, especially when it comes to birthdays which are inevitable, technically, whether you're alive or not but there are times when the meaning changes more so than this.
Generally, "would have been" would apply to that particular event at that particular point in time. It's something that was likely or known to be planned but didn't happen. "Would be" is speculative without the implication that it could or should have happened.
Think about two parents who lost a child in a car accident a few years ago.
"He would have been a college student this month." - They know he was going to become a student but he's not now, because he's dead. It was supposed to happen but didn't.
"He would be a student this month." - It's possible that he would have become a student but it's less decisive or sure as the previous example. It doesn't as strongly imply that he was "supposed" to do it. The previous example is a sure thing. This one isn't.
I think the implication changes because "have been" implies an ongoing state of being while "be" does not... but that interpretation may vary from person to person.