It's all a matter of perspective. I would make sure to clarify, or ask someone else to clarify what they mean by whichever term they are using.
For instance, Alexis' answer seems to be well researched, and I would not argue with him - but the terms mean different things to me.
In Alcoholics Annonymous, an alcoholic is plain and simple - someone who does not have control over their drinking. By not having control over ones drinking, we mean - once you start with that first drink, you can not stop; you lose control. This is manifested by not being able to stop drinking after the first few drinks. Someone who is not an alcoholic would have no problem doing so, and may find it harder to keep drinking than to stop. The alcoholic will almost always drink to the point of blackout and most likely cause problems for himself and those that he is close to.
Alcohol abuse on the other hand is a little less severe. When I hear alcohol abuse, I think more about college kids getting plastered than I do about people whose life has been ruined by drinking.
Needless to say, you will hear the terms used interchangably and everyone will have their own slightly different version of what the two phrases mean.
A common definition of an alcoholic is someone who drinks every day, who needs booze to function. And while I dont argue with this terminology, I think someone could still be an alcoholic without having the dependence. Hence, you could state the phrase, alcohol dependancy.
For a short and sweet answer, alcoholism, I believe is "worse". Alcohol abuse can lead to alcoholism.