I don't know, if you look at successor nation states to big empires, they are usually less warlike. Examples include the Austro-Hungarian Empire and the Soviet Union. I mean when was the last time the Czech Republic started a war. Even if you look at Yugoslavia, the violence could be seen more as a reaction of being conglomerated together rather than nation-states fighting each other.
Also the European Empires fought the bloodiest conflict in history other than World War II and it can be strongly argued that World War II would not have happened without World War I, so I don't think your argument that nation-states are more violent than empires is sound.