I am not sure if Civ4 would provide for such a distinction as urban-rural population. It could just be that cities would count as administrative centers for predominantly rural provinces.
Indeed you have a point. I don't know if we can reach a form of analyzis to tell which are the criteria to account urban population in comparison to non-urban population.
If we take into consideration Cottages and their evolutions, Baghdad (Babil has changed name to Baghdad folks, this will be done ingame as soon as the term is played) would have a big urban population because it is currently working 6 cottage-like improvements (1 Cottage, 2 Hamlets and 3 Villages).
But we should also presume that people assigned to water tiles should be based on the city itself rather then another land tile (and obviously they aren't sea-people living in the water tile itself, like some sentient fishpeople on some islands in the pacific that we heard about long ago

). So these should also be accounted as urban population because they should be living in the city tile itself.
The most problematic point would be the exact number of population (not pop points). Fo each pop point the number of people in the city and its vicinity increases exponentially, so it'll be really hard to normalize this value for comparison. E.g. Al-Quds is a 11-pop city and has 1,331,000 population which is almost the double of the 729,000 population that As-Sur has and As-Sur is a 9-pop city.
Let's try something, let's Compare Baghdad and Al-Quds:
Baghdad Al-Quds
1,000,000 Population
1,331,000 Population
1 used Cottage
0 used Cottages
2 used Hamlets
2 used Hamlets
3 used Villages
0 used Villages
0 used Water Tiles
6 used Water Tiles
If we consider all other tiles to have non-urban people (farms, oasis, mines, forests, quarries, plantations), then Baghdad has 6 urban pop-points and Al-Quds has 8 urban pop-points.
But Villages should have more people then Hamlets, and those more then Cottages, and maybe the population living in the capital working a water tile should be less then the people living in a Cottage tile. Specialists could have the same weight as Water Tiles. If we transform these into values we could use:
Another factor I would like to call in is a 10% of all pop-points assigned to non-urban areas to be accounted as urban pop. This would represent people living in the city itself that are related to what is done in the non-urban tiles (merchants, distributors, politics, all their personal staffs, etc.).
Then we sum all pop-points (with their values, non-urban will all account as 1.00) and divide urban/non-urban accordingly from the total population value. Then we get 10% of non-urban and throw into urban. Let's try this out:
Baghdad Al-Quds
4 Non-Urban Tiles Used
3 Non-Urban Tiles Used
10.25 Urban Factor
9.00 Urban Factor
71.92% Urban Pop
75% Urban Pop
10% of Non-Urban = 28,080
10% of Non-Urban = 33,275
747,280 Urban Population 1,031,525 Urban Population
So
Al-Quds has yet more urban population then
Baghdad, and I would presume more then any other city in the Caliphate (because I believe Baghdad was the only that could possibly compete with Al-Quds for its extensive cottage-like vicinity).