I have quite a few characters on either side. From my experience, I've noticed a lot of the empire non-class missions are about subjugating uprisings, sabotaging both republic efforts and the plans of opposing rivals within the empire. Many of the missions put you in a situation where you can choose personal benefit or helping the empire as a whole or helping an individual benefactor. On the republic side, many of the missions are about repairing damage the empire has caused, striking back at them, helping locals, walking the grey line between selfless and selfish, etc. Personally, I think the empire classes are cooler, but the mission quality is about the same.