See Warsaw. Because river is not regulated (I think that's the only european capital with unregulated river going through) and there are only few bridges across it divides the city more than usual river does. Left, west side is classic downtown with skyscrapers and stuff, and right, east side, called Praga, is filled with low buildings and is much more green. And also poorer. The difference is most apparent on the riverbank. West side has some river boulvards and buildings right next to the river, while east side is literal forests and beaches.
Moreover, the west side was completely destroyed during the war, so all buildings are 50 year old max, while east side is filled with pre-war buildings. The rebuild Old Town is thus younger than the normal town on the other side of the river

. The differences start to fade as the time goes and further from the city center but generally western side has much better infrastructure and population density than eastern one. It's a vicious circle really, because one side has more people, it gets more infrastructure budget which makes it more attractive to live in and thus gets more people and so on...
some pictures: