PRH, All empires flourish with legitimacy and decline with the loss of legitimacy.
I think the politics is dependent on two aspects: power(Bhayam) & perception(Bhakthi). There seem to be only two ways to keep followers loyal: Bhayam(terror) or Bhakthi(love/respect).
The goal of power projection is to create terror or deterrence: Bhayam.
The goal of perception and propaganda is to create loyalty or love: Bhakthi.
Power == hard power == armed men.
Perception == soft power == culture, religion, language, food, ...etc.
Money and technology are somewhere in between these two groups. Money and technology facilitate both Power projection and better perception. So, they are facilitators.
Ideally, the enemy should be deterred by the leader and followers should respect the leader. But, it is easier said than done. Most of the times, leaders find it easier to terrorize their own followers than to terrorize the enemy. Because the leaders have more power over their own followers than on the competitors or enemy.
Here is a related question: Why does every invading group inflict extra-ordinary cruelties on the local people?
I think the idea is simply to terrorize the people into surrendering. Generally, the invaders are smaller in number than the locals. Further, the invaders are in a foreign country unknown to them. They are afraid of losing control if they have the control in the first place.
The easiest way to get power and keep it in such circumstances, is to terrorize local people into surrendering and remain surrendered. To terrorize people, the idea is not to just kill but do things which make the locals really really terrorized. Yes, its cruel method.
The terrorizing method works but its a very difficult method to implement properly apart from it being very cruel. Too little terror, and the people fail to be terrorized. Too much terror, and people are so terrorized that they become desperate and ready to rebel.
Only rare invaders who are naturally superior in numbers/power/culture would have the strength to co-opt the locals: Bhakthi. If an invader can progress from Bhayam to Bhakthi level, that itself would be a huge success and signifies consolidation of power. The same applies to any leader.
Now, which empire would flourish depends on relative power and relative perception compared to the other competitors.