The Romans seemed to be ahead of their time, a society that accomplished feats of great magnitude. So when was society in Europe back to that certain degree of sophistication and order. The years that followed had Europe in the mess that is Feudalism but that ended around the 1500's and the continent became richer by exploiting the Americas. The industrial revolution brought great innovations that the world had ever seen including the great often taken for granted modern sewer system. So truly my question is after Rome, when did Europe became awesome again?
There's certainly room for someone to write you a full response, but you may be interested in these previous questions/answers:
Did the Catholic Church hold back scientific and technological progress in the Middle Ages?