As mentioned already, Constantinople was a multicultural city. The Turks were only a minority in the city before WW1, and the the city declined enormously (in population and in wealth) after the war as the Turks expelled / pogromed most of the Istanbulite Greeks, Jews and Armenians in the 1920s-1940s. Population numbers can be found here: https://en.wikipedia.org/wiki/Istanbul#Demographics
AFAIK it took until around 1950 for the city to return to its pre-1914 population, and by then most of the newcomers were poor illiterate people from the countryside, so the face of the city had changed enormously. It was poorer than it had been, and much less cosmopolitan.
If the Greeks took control, the same thing would have happened, more or less: There would have been expulsions and pogroms against Muslims and eventually also Jews, Armenians and other minorities, leading to a drop in population of maybe 20-40% over a course of 10-15 years and a hemorrhaging of wealth, while simultaneously they would try to attract diaspora Greeks to repopulate the city. That being said, the city was big but it was not actually a huge metropolis by continental European standards - its population at the turn of the century was perhaps 900,000 people, of which something like a third were Greeks and another third were non-Muslim minorities (Jews, Armenians, etc), so it would not be beyond the capacity of the Greek government to remove the Turkish element of the population and turn it into a majority-Greek city relatively quickly. Greek society after WW1 was rabidly and violently nationalist, but it did not become as culturally insular as the Turkish republic, so Greece might actually have been a little more benevolent towards minorities. Who knows. But since Greece is overall a smaller country, Constantinople would under Greek rule probably not have seen a population explosion in the 1970s and 1980s like Istanbul did.
