I have been taught that sometimes the only amends is to be a living amends. For me that means that an apology is not necessarily the best thing. Many times an apology can be too easy which leaves the behavior still there. Changing the behavior is what counts. With my children I have to do a living amends as I spent too many years while drinking apologizing to them....today the only way I can make sure they see I am truly sorry is by changing my behaviors. It is through this that I have been able to rebuild a solid relationship with my two oldest children after drinking my way through most of their lives.
I do however believe that if one can both apologize and change the behavior that is the best thing to do.