Tang was never a military power house. it is known for its culture and science. Song was small and weak beacuse of all the boarder confilct with other chinese ethnic groups. and none of those nations during Song era was really big and well funded. thats why mongols just rolled through them all. Of course the mongols were amazing too.
It basicly should boils down to: Han, Ming, Qing. Han is 3rd largest dynasty ever at its peak if you count in yuan. and during its time Kao Tsu, wudi and other empreors have expanded the boarder and opened up trade routes.(the silkroad) For its time it was no doubt one of the great powers. Even the Romans at the time couldnt match them.(206 b.c. - 220 A.D.) At that time the Romans were involved in Macedonian Wars. And these wars for the most of time were at a small scale thats fought between Greek city-states, and Syria. Kao Tsu also pushed out the Huns that was in western china and beyond, which enabled the silkroad to be open. Huns later dominated most of europe and the Romans couldnt really stop them. So in terms of territory size and amry size and technology Han at its time was far greater than any nation.
As Ming and Qing, I think FriedRiceNSpice explained pretty well on why it was a great military power.
The problem with most Chinese dyansty is that none of the rulers were ambitious enough. Han, Tang, Ming even part of Qing could easily conqure every other nation near by. And project its power over europe and even find america. But due to that they never got anywhere. and even for the ones that did explore, and seeked out others. because of china's technology were so much more advenced compare to other powers at the time. The explorers comes back with nothing new, and the king/empreor would assume that every other nation around the world are nothing compare to him therefore compeletly ignore other nations, unless they come to him. Over the time this settles in and became the close door policy. And China became more and more isolated and shortsighted that it stop most of technological and civil advencements. Until rest of the world caught up and surpassed them.