Aggressors are, by nature, the highest damage dealers in the game. Almost without exception, their sole purpose is to cause damage to enemy heroes. Some bring more utility than others to battle, and several have synergies that assist their allies, however the overarching theme for aggressors is to kill enemy heroes.
Whilst there are no hard and fast rules around Warband selection in Judgement, it is only the most experienced of players that venture on Between without 1-2 aggressors in their Warband. Do to be fooled however, because not all aggressors are straight forward to use, and will take some time to master.