Would the Byzantine/Eastern Roman Empire be considered more technologically innovative or conservative? I've seen different representations of this popularly - in video games such as Medieval II: Total War, they are on the conservative side, with little to no gunpowder technology into the 1500s (although, admittedly, this may be the developers' not putting in units that never existed), and in Paradox Interactive's Europa Universalis IV, Byzantine technology advances less quickly than the French, English, or Spanish, instead being on par with the Hungarians and Russians. However, in another Paradox game, Crusader Kings II, the Byzantines have a technological advantage over feudal Europe. In more grounded terms, I know that Greek and Roman learning was much more well-preserved in Constantinople than it was in western Europe, and things like Silk Production, Greek Fire, and a Centralized government were all more advanced in Byzantium than they were in western Europe. However, I've also read that they failed to see the advantage of gunpowder weapons in the Siege of Constantinople.
So, my main question is: would the Byzantine/Eastern Roman Empire be considered more technologically conservative or innovative? Of course, this probably would be different in different time periods of their history. As a secondary question (although I realize this is probably more speculative history) is, in a surviving Byzantine Empire (with relatively comparable nations in Western Europe), would they be capable of keeping up with England, France, Spain, and Portugal technologically?
I would argue that essentially no one in this period -- except maybe Southern Song China -- was very innovative at an intentional, scientific level. Innovation happened sporadically, but I'm not sure that I'd say anyone was "innovative" in the way that, say, Apple likes to call itself innovative: actively looking for new ways of doing things.
In terms of practical technological advances, such as the development of the three-field agricultural system and good, seaworthy sailing ships (cogs), I would say that Western Europe was possibly the most innovative region -- oddly, perhaps more so in the "Dark Ages" than in the "High Medieval." The Western Europeans did not have a very sophisticated, literate civilization as a whole, but they were coming up with new practical lifehacks faster than the more urban, learned civilizations of the Byzantines or Abbasids.
Note: the above was based on a misremembering of sources. Dark Ages Western Europe was not a realm of practical innovations to the extent that I had misremembered. Western European inventiveness became prevalent in the 1000s.
In terms of theoretical science, the Islamic world lead the way. They were making advances in understanding astronomy, mathematics, chemistry, medicine, etc, such as categorizing various illnesses such as smallpox and measles and developing algebra.
The Byzantines? They adopted new technologies they found useful where they found them, but as a whole, they didn't develop either the sort of practical improvements to their west or the kind of theoretical advances to their east.
However, technological differences were fairly small throughout Eurasia, at least at the level of actually knowing the principles behind something. Organizational capacity and wealth were far more important to being able to actually implement advanced technologies. There were undoubtedly people in the Carolingian Empire who understood the principles behind building an aqueduct (millennium-old tech), but actually being able to organize and finance the construction of such a project was another matter. The Byzantines generally had a fairly well-organized state, so in practice, the range of technologies they could really implement could well be wider than some Ottonian duke.
As for gunpowder in particular, the first recorded Byzantine use of gunpowder weapons (1396) was before the first Turkish use. At the 1453 siege of Constantinople, though, they faced the problem of a severe lack of resources to actually implement much of anything. This time, it was the Byzantines who were in a position like that of a Dark Ages Ottonian Duke -- all the theoretical knowledge in the world wouldn't help them if they didn't have the resources to make use of that knowledge.
This is not a historical answer, however I would like to answer from the game standpoint as someone that has played those games: It's just for balance's sake.
In Europa, the way technology works is simply that if you are not western, you get a tech malus, and so the byzantines were lumped in with the rest of the eastern European nations due to the way the tech borders were drawn (map is 1444, if anyone is interested).
I personally wish they had gotten their own technology group, separate from western/eastern, a little like how the Ottomans have their own technology group, but Paradox probably figured that a state that only has three provinces at the start of the game wasn't worth the hassle of programming another tech group. After all, you'd need to make a whole new set of unit for a tech group that would be unique to a state that isn't even important for the vast majority of that time period(1444-1821).
EDIT: I would also like to add that Crusader Kings covers roughly from 867 to 1453 while Europa covers 1444-1821. That would greatly explain the difference in the representation of the Byzantine Empire from one game to the next.
