The interesting thing is that we are accustomed to forget about Eastern Medievalism - not to think of Constantinople/ Byzantium as part of the Medieval era; and I suppose the reason is not just its being geographically cut-off from the West, but more fundamentally that the Eastern Empire actually was not 'medieval'; that is, it was not a 'Middle Age' but was a continuation of the ancient world - because the East had not experienced an intervening Dark Age to separate it from the Christian Roman Empire.
So the proper comparison is not 'Medieval', but between a continuation of Classical Civilization in the East, and a new-born, new-built Christian civilization in the West - the East being focused on the great city of Constantinople, and the West probably best exemplified by France, and especially Paris and its University with figures such as Peter Abelard then Thomas Aquinas, Duns Scotus etc.
Despite natural patriotism, my heart warms to the East, because the distinct focus of life in the West (according to CS Lewis) was scholastic philosophy - about which I am ambivalent at best; the Crusades - only the first of which was sincere; the cult of courtly love - which I loathe; and the great Cathedrals, which I love unreservedly - but which I suppose were at least matched by the mostly-lost beauties of the Eastern Empire.
What did the Eastern Empire have? The Emperor, as Vice-Gerent of God; and from him the ideal of life as a seamless Christian whole - such that Christianity permeated society in the most complete way ever achieved on a large scale and sustained over centuries.
Of course there was much to dislike too. I feel that the ascetic ideal became perverse in its extremes; there were stupid heresy hunts, silly pseudo-schisms, and vile suppressions; and ultimately - for all its intoxicating qualities, and its great strength to endure and inspire resistance - I sense there was something profoundly demotivating and despairing at the heart of the Eastern Empire.
I get a sense of living always under the shadow of impending doom, rather like the theory of courage of the Northern Pagans with Ragnarok.
Both civilizations shared the typically medieval bipolarity of ascetic, virgin celibacy on the one hand and as the highest ideal; and a sumptuous 'dripping with luxury' aestheticism on the other hand ...ascetic-aesthetic'; light-dark; spartan-excess; fasting and feasting...
This was the Way of Negation: Christianity by means of denial and then lapses, and recreations from that strenuousness.
Psychologically, this is a young man's concept of the world, the unattached and solitary consciousness; a perspective which lacks any serious interest in in the mature man's natural and proper focus on marriage and family - rejecting the Way of Affirmation as Charles Williams dubbed it - rejecting marriage and family as second rate and a compromise: what moderns call a 'sell-out'.
In a nutshell, Medieval life, both East and West, lacked sweetness.
And it lacked sweetness, because sweetness is about (derives-from) faithful and loving monogamous marriage and even more so from Life (specifically Christian Life) conceptualized primarily, or ideally, or in its highest and best form, as family life with children.
As briefly as possible: the essence and ideal of sweetness comes from loved and loving children.
In this sense the post-medieval world has - in some times and places - out-matched all the ancient times; has a higher, better, more wholesome ideal of Life and in particular of Christian Life.
And from this perspective, Medieval and Classical life seems - and indeed really was; for all its splendour, courage, intensity - shallow, incomplete, and terribly sad.