However--while it seems to me that certainly there were aspects of Medieval society that were advanced--even some that were superior advancements over what the ancients had achieved in Antiquity--overall, much of Medieval society was decidedly more primitive and less developed than society in Antiquity.
Now that I got the East Asia stuff out of the way, it is time for the Medieval European Historian in me to get to work. While an incredible amount of knowledge was lost due to the fall of the Western Roman Empire, it is completely wrong to assume that the Middle Ages was a time of technological and cultural collapse. In fact, a number of technologies that were considerably more advanced than anything seen in the Roman Empire had appeared in Medieval Europe.
Military:
The technological achievement of the armored knight should not be ignored. First off, it requires something the Romans never had: the stirrup, which appeared in Europe in the 6th century. It was the stirrup that enabled cavalry to become a major factor in warfare. Furthermore, weapon and armor technology came a long way during the Medieval period, which eventually saw the rise of steel plate armor with extremely sophisticated articulation.
Europe also saw a remarkable increase in the technology of both castle design and in siege weapons. For example, the trebuchet was not available to the Romans.
Agriculture:
Here is the big one. In the Early Middle Ages, for a time, the best plow available was the Roman plow, also known as the scratch plow because it was only capable of scratching the surface of the soil. In the 6th century AD, the iron plow was adopted in Europe. This plow was capable of digging much deeper into the earth and creating much better fields. This technological advance was paired with the introduction of the horse collar, which increased both the load capacity and endurance of horses and oxen used to pull plows and other heavy loads.
Combined with new crop rotation techniques and other agricultural improvements, this led to an agricultural revolution in Medieval Europe that triggered a major population boom.
I could go on further, but I would need to dig up my notes from out of storage.
About the idea of Roman Circuses versus European tournaments though...
The Roman circuses and gladiatorial events were much like really violent versions of modern boxing matches or races: they were primarily competitions between small numbers of individuals as entertainment for a local crowd. Even the Coliseum's influence was mostly confined to Rome.
The grand tournaments of the 11th century were a completely different beast altogether. A medieval tournament was where a few hundred to a few thousand knights from as far away as Britain, Spain, and Germany would come a town in Northern France, split into two armies, and then charge each en masse and begin a day-long battle using weapons that were merely blunted. The annual tournament circuit of Northern France could be considered a series of mock-battles, designed more to train knights for actual warfare than entertainment. Though it was the most popular form of entertainment in Europe, despite various monarchs' attempts to ban or control it. The international popularity of the tournaments was such that a certain British prince who spent a fortune on tournament teams became a household name in France. Furthermore, the amount of money put into tournaments led to the rise of professional tournament experts and commentators: the heralds.
It is safe to say that the grand tournaments were not small, local affairs. Is it obvious that I wrote a term paper on this topic?
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