I live in Birmingham, and i really dislike it as a city. It is very segregated, with areas such as Sparkhill, Sparkbrook, Small Heath, Aston being 85+% non-white, and areas which are somewhat the opposite. Combine that with a lot of people in the city centre, pretty high crime rate, and what is voted one of the worst regional accent in the UK, and you're onto a winner.
For a student lifestyle, i think that Southampton would be by far the better.
Then again, just my personal opinion from my experiences in Brum.