"Today is Joe's birthday" or "Joe's birthday is today"

There is only a very slight difference - so slight that it is almost nonexistent. Today is Joe's birthday puts a subtle emphasis on today, since we began the sentence with today, and so today is the thing we're talking about. However, when you start with Joe's birthday, that becomes the main point of the sentence.

The reason why there is almost no difference is that Today is Joe's birthday automatically draws attention to the birthday part, whether the sentence began with it or not. There are so many todays, but not that many Joe's birthdays, so we instinctively think Joe's birthday is the point of the sentence, not today.