you have to do both.
start off with your rebuttals of the other side's arguments. this means you directly clash with whatever affirmative said. then go on with your own arguments. they may be based on the aff's disadvantages or your side's advantages as you said.
though be careful about negative argumentation. if you just keep mentioning their disadvantages without forwarding the benefits of your side, it doesnt give you as much credit and makes you look weak.
hope this helps.