The thing about apologies is that they are all fine and good when the person apologizing actually knows what they are apologizing for. Giving someone a blanket apology, one that is meant to cover "whatever it is I must've done" is simply a cop-out and not the true intent of what an apology is really for. When one apologizes, it is supposed to be about feeling and emotion. One must truly understand the wrong, truly feel the hurt of the other person, and truly be sorry for the offense. The problem that most apologizers have is that they haven't a clue what they are sorry for. Hence, the empty apology.
So really what is worse - the initial hurtful action or the fact that the one apologizing simply hasn't a clue that they've acted in such a manner as to hurt another person? Only when one completely understands and feels badly for where they have misstepped can one wholeheartedly expect an "apology accepted."