Wrote a little novel by accident, hope it's some kind of helpful.
Answering your question, I will follow these steps:
- Which cities have been the largest between 1000-1500 a.D.
- How have they become so large?
- What have been their main problems which impeded further grow?
The largest medieval cities per population.
Baghdad is often declared as one of or even "the" largest medieval city in the world. Between 900 and 1400 the population often raised and dropped between 150.000 and (according to some sources) 1.200.000 citizens.
George Modelski, World Cities: –3000 to 2000, Washington DC: FAROS
2000, 2003. ISBN 0-9676230-1-4
150.000: Tertius Chandler. Four Thousand Years of Urban Growth: An Historical
Census (1987), St. David's University Press (etext.org). ISBN
Compared with Baghdad, Hangzhou steals the show.
According to the Encyclopedia Britannica, Hangzhou had a population of over 2 Million people in the year 1276. This number is a rough estimate and not proven. Local authorities numbered 186.330 families ( with 5-10 people per family ). Thing here is, that they probably failed to count non-residents and soldiers living in the city too. Only registered citizens were counted.
However, Hangzhou was surely the largest city of its time with 1-2 Million people.
"Largest Cities Through History". Geography.about.com. 2011-03-02. Retrieved 2011-03-16.
Janet L. Abu-Lughod, Before European Hegemony: The World System A.D. 1250-1350, "All the Silks of China" (Oxford University Press US) 1991, p. 337
How have they become so large?
Baghdad has an excellent location. Controlling strategic and trading routes at the Tigris, as well as superior water supply.
Looking at a map from ~900 a.D., water is not an issue at this location.
Baghdad was built in just 4 years by roughly 100.000 people from all over the (known) world (Europe, Africa, Asia), with such an effort and budget, that it soon got the reference to the Qur'an's paradise. The fast growing young religion Islam supported the city's growth, as people want to get their place in any kind of paradise.
Due to this role in the Islamic world, Baghdad had to handle massive immigration and this grew fast. Soon it had evolved to one of the largest centers of trading, religion and knowledge.
Baghdad was what Rome had been 1000 years ago, just more modern.
Is another piece of paper. Founded in 328 b.C., it grew slowly but steadily. While Baghdad was planned with a massive wall, Hangzhou got it's city wall 900 years in existence. At this time, it started to grow more rapidly.
The grand canal was built from Bejjing to Hangzhou which established Hangzhou's critical role in Chinese trading culture. In the 10th century, Hangzhou had an explosion of culture, after it became the capital of the Wuyue Kingdom.
But the REAL flush of population began in the first years of 13th century, when mongols conquered large parts of china. Millions of refugees were searching for safe places and Hangzhou, with his massive walls, seemed capable for many people. In 1275, several decades after the first mongol attacks, the population had been ca 1.750.000 people. In 1276, when the mongols conquered the city, the population dropped immediately.
Monica Cable (1996), "Hangzhou", in Schellinger and Salkin, International
Dictionary of Historic Places: Asia and Oceania, Routledge, ISBN 9781884964046
What have been their main problems which impeded further growth?
You might accept an excessive answer, but there's none.
Sure, both cities struggled with the same problems as any other megacity of this time, but the real issue was war/politics.
1276, Mongols conquered the Chinese megacity. The story of successful growth has gone in another row after they left. Today, Hangzhou is one of the largest cities in the world, with ~21Mio people 2011, according to the Chinese census.
Baghdad on the other hand, struggled with the raising Caliphates power. 1058 it had been conquered by the Turkish general Abu'l-Ḥārith Arslān al-Basasiri and since then, it seems like Baghdad has become a playball for every warlord in this area.