I look at aggression as an emotional state, rather than the capacity for violence. Consider the army. Soldiers are expected to commit violent acts on enemy soldiers, yet they are also expected to maintain emotional control. They are typically expected to avoid killing civilians. They are certainly expected to avoid killing friendly targets. Clearly they have a capacity to commit violence and I suppose most people would say there is a need for aggression because of that. On the other hand, they are not aggressive in the sense of random acts of violence (as would be the case of a bear or a raccoon attacking a bystander).

It's just a job, and the decision is backed by justice.

The guy who kills a family for fun is more aggressive than the guy who execute him. I'm not even sure how you could get to any other conclusion

No, they are not. I think, on average, those who execute are much less aggressive than those who are executed.