Ming Dynasty and Ching Dynasty armies were extremely powerful. So were Japanese armies in that 1500s/1600s time period. The Moghuls, the Sikhs, the South Indians... the Moros, the Afghans, the Mayans... they were all people who could fight and adapt. Their reasons for NOT restructuring their war doctrine was that, for their own geographic location, they didn't necessarily need to. The Ming Dynasty had a military that ranged from crack cavalry battalions and musket regiments in the north, to 11-man squads in the south. They had a good navy and were all well-organized. Look at Zheng Cheng Gong (Koxinga), he had an appreciation for modernization and had he succeeded in creating a long lasting Ming state, you'd probably see a sea-faring, gun totin', modern military system guided by a regime interested in trade, modernization, and expansion - everything the Ching was not after they had conquered Tibet and Mongolia along with China. The Moghuls and Sikhs are a good example of folks who didn't update their war doctrine enough, but had very good troops and were on their way to modernizing their armies. I could explain the others, but I think the Moro resistance to the Spanish and Americans, and the Caste War of the Mayans speak for themselves.
It's not 'European' that made them powerful. It was 'adaptive' that made them great. China and India have had firearms for a LONG time. But eventually they were importing or copying European firearms. Why? They stagnated in their own technological evolution. Their rulers cared more for their large land-based countries and agriculture than sea-trade and dispersal of ideas. And many cultures were caught in a bad time, where-as the Europeans were at a peak. I don't blame the Europeans. Had the Chinese put their hearts to it, they could have conquered a lot of S.E. Asia, as well as Mongolia, Korea, Tibet, etc. But they never had a great incentive to (in their own eyes). Those who did not understand the need for evolution, may have been great warriors, but often could not face the better armed opponent. In-fact the Europeans faced MANY capable warriors in the peoples they conquered. Just for thought. Indian and Chinese histories from 0 to 1500 AD tell of a lot of conquest and supremacy. The stagnancy is a new thing for cultures that have been prosperous and progressive for a long time.
just goes to show, if you don't get up and do stuff, the world will pass you by... and maybe take your land and make you labor for them.