It doesn't really have an American equivalent. If I had to name a city, I'd go with Baltimore--Horrible reputation (But the history of police clashes isn't nearly as bad in Birmingham as Baltimore), a lot of closed factories and general economic decline since deindustrialisation and a strangely successful Symphony Orchestra and Hippodrome. However, Birmingham's bigger, has more rain, some canals which are either amazing or disgusting (depending on when and where) and the universities are a good deal better