Westeros, the place with all the white people, is the most powerful nation in that world
Westeros is as much a "nation" as the Holy Roman Empire. The Seven Kingdoms, as implied by the name, aren't very unified, and even this low level of centralization has only been the case for 300 years. Before Aegon's Conquest, the various kingdoms were independent and waged constant wars with one another, and even after the Conquest there was still the occasional civil war and lots of instability.
As for power - far more powerful empires have existed, like the Great Empire of the Dawn (although that one's possibly mythical), the Valyrian Freehold, the Old Empire of Ghis, and one still exists - the Golden Empire of Yi Ti. Seeing as Yi Ti is basically fantasy China, it would probably be the most powerful state, although it seems that at the time the books are taking place it's been pretty weakened. Westeros however definitely isn't the most powerful "nation", because it simply isn't a unified political entity - some of the individual kingdoms might be considered to be powerful, but not the whole continent.
while the continent with all the brown people is mostly made up of disparate city-states and warlike savages
While I definitely agree that the Dothraki are a pretty dumb portrayal of a steppe culture, those disparate city-states are quite wealthy, and powerful at least in an economic sense, if not a military one. They are also arguably more culturally developed, if we consider an oligarchy of merchants to be more developed that feudalism, and while they may be disparate now, most of them trace their origin back to the Valyrian Freehold, which controlled all of their territories and more as a unified state.
Besides, there's more to the further east of the continent - Slaver's Bay is also incredibly wealthy, and similarly used to be part of a unified empire until it collapsed. There's various states around the Bone Mountains, and Yi Ti even further east.
Europe was a balkanized backwater while the Islamic world was a cultural powerhouse and China was already a thousand year-old empire
That's basically the case in ASOIAF. Westeros IS and has historically been a balkanized backwater, while the Free Cities are more politicaly and economicaly developed and used to be part of one of the world's greatest empires, and Yi Ti has been around since the Long Night, with the Great Empire of the Dawn that it (allegedly) succedeed being even older.
Westeros is as much a "nation" as the Holy Roman Empire. The Seven Kingdoms, as implied by the name, aren't very unified, and even this low level of centralization has only been the case for 300 years. Before Aegon's Conquest, the various kingdoms were independent and waged constant wars with one another, and even after the Conquest there was still the occasional civil war and lots of instability. As for power - far more powerful empires have existed, like the Great Empire of the Dawn (although that one's possibly mythical), the Valyrian Freehold, the Old Empire of Ghis, and one still exists - the Golden Empire of Yi Ti. Seeing as Yi Ti is basically fantasy China, it would probably be the most powerful state, although it seems that at the time the books are taking place it's been pretty weakened. Westeros however definitely isn't the most powerful "nation", because it simply isn't a unified political entity - some of the individual kingdoms might be considered to be powerful, but not the whole continent.
While I definitely agree that the Dothraki are a pretty dumb portrayal of a steppe culture, those disparate city-states are quite wealthy, and powerful at least in an economic sense, if not a military one. They are also arguably more culturally developed, if we consider an oligarchy of merchants to be more developed that feudalism, and while they may be disparate now, most of them trace their origin back to the Valyrian Freehold, which controlled all of their territories and more as a unified state. Besides, there's more to the further east of the continent - Slaver's Bay is also incredibly wealthy, and similarly used to be part of a unified empire until it collapsed. There's various states around the Bone Mountains, and Yi Ti even further east.
That's basically the case in ASOIAF. Westeros IS and has historically been a balkanized backwater, while the Free Cities are more politicaly and economicaly developed and used to be part of one of the world's greatest empires, and Yi Ti has been around since the Long Night, with the Great Empire of the Dawn that it (allegedly) succedeed being even older.