I've lived in both and Manchester is a much much better city for culture. Loads of gigs going on all the time, places for independent cinema, events, great comedy nights etc.
I think Birmingham wins when it comes to restaurants and eating out.
Driving in Manchester is an absolute nightmare though, traffic everywhere all the time.
Also the reputation of it raining all the time is absolutely bang on. One of the main reasons I left Manchester and came back to the Midlands was I couldn't handle the rain anymore.