The comparison does not really hold: you would be hard pressed to find a single first point of contact between Goths and the Roman Empire or Mongolians and China.

In both cases, fighting had been going on for centuries before the empires were finally toppled. Thus even if overall less advanced, the "barbarians" had comparable warfare technology.

In most known cases where a true first encounter event occured - such as Columbus arrival in Hispaniola, Pizarro in Peru or Cook in Australia - the less advanced civilization was indeed overrun if not exterminated by the more advanced one.