An oppressor first uses military in the short term to dominate a country and the uses cultural change in an attempt to bring about any long term changes in life style, etc. Miltary is short term change but culural revolution can bring about the most long term effects, thereby making it more powerful.
Cultural domination is most often on going and long lasting, sometimes permanent. Military domination is most often short lived in comparison and usually contributes to its own demise in the long run. In China you have a good example of both and in combination. Though China has military domination, its real culture far exceeds it in length of life and is centuries more dominant. China is a cornucopia of fantastic and rich cultures, the likes to which few countries have ever matched over the ages.Culture is reflective of the people that live in a country and military applications are the product of a few weak and fearful beings who frantically seek ways to take short cuts and control others by fear. It is short lived and eventually unsuccessful as the dictators or power mongers fall from grace in a relatively short time. Hitler, Napoleon Bonaparte, Mussolini, and others,as examples, fell victim to their own ruthlessness in time.
I say cultural domination. Military domination is binded with the country laws which is always prone to discrepancies while cultural domination is binded with culture, belief and oftentimes faith. A society binded with culture is strong and powerful.