First I'm not sure "suffered" is exactly the right word, as opposed to "experienced". The Turkish economy seems overall to have benefitted from the steady population growth and massive urbanization of its population over the past 90 years.

Greece also experienced massive population growth over that same period: from some 6 million 90 years ago to some 11 million today. The population has remained more or less level for the past 20 years or so. With the 20 year rule, that limits the ability to discuss any changes since that time.

Despite being neighbors, Greece and Turkey went through very different experiences in the later 75 years of the 20th century from each other. Greece experienced foreign occupation in World War II, accompanied by mass killings and a massive famine that killed an estimated half a million civilians. This was followed by a brutal civil war, a repressive military junta from 1967 to 1974, and then a return to democracy and a sharp turn towards the European Economic Community and subsequent EU.

Which is to say, at various points in modern Greek history, there have been massive events causing death, dislocation, and emigration (remember that there is a relatively large Greek diaspora worldwide, and this predates the 20th century, which is also a strong pulling factor). While Turkey has had its fair share of troubles, it did not directly experience the Second World War or a major civil war (the Kurdish Insurgency, for all its death and displacement, is relatively localized and has affected a proportionately smaller part of the population than the Greek Civil War did). Its population growth largely pushed on at a steady rate throughout the 20th century.

Turkey also has had a lot more literal space for urbanization over this period. Much of Greece is mountainous, or islands and peninsulas and not well suited to expanding one's cities. Turkey is just a lot bigger - the Central Anatolian Plateau region, just one of Turkey's seven main geographical regions, has more land area than all of Greece combined. While Athens has grown into a large metro area (3 million people), Istanbul has at least 10 million more people than that: it just has a bigger hinterland to expand into, and a larger rural population to draw into the city. After Athens, Greece only has one metro area over a million (Thessaloniki) - and then metro areas drop off precipitously in size (Patra has about a quarter million). In contrast, Turkey easily has 12 metro areas over a million people

Even though Turkey and Greece both transitioned from rural to urban populations at about the same rates over the latter 20th century, and although their fertility rates similarly declined over that period, Turkey was just bigger, and that tends to add a certain inertia to demographic trends. It's also worth noting that in the past 30 years the Greek fertility rate has fallen more than it has in Turkey, although even in Turkey it's at or below the "replacement level" of 2.1. I'd defer to another contributor who would know more specifically around the drivers of these declines.