The two unis are pretty similar in many ways - Russell Group, near a city centre and large.
I've never been able to understand the hype about campus unis though - very often the only real distinction between the two seems to be that campus unis don't have outside traffic passing through them. Manchester is classed as a city uni, but all the academic buildings are really close together, and it's on the busiest bus route in Europe, which makes travel super convenient.
Some of the accommodation at Manchester isn't hugely aesthetically pleasing, I'll grant you. However, you need to take into account that you'll only be living there for one academic year (7 months of term time), whereas you'll be spending three years at the university as a whole. All UoM accommodation is fundamentally sound (i.e. you're not going to have problems with damp or vermin). I can assure you that when you look back on your time in halls, what you remember won't be how aesthetically pleasing the kitchen was - it'll be the people you met and the experiences you had. There's some more info and photos about UoM halls at
http://www.thestudentroom.co.uk/showthread.php?t=2091577 One good thing about Manchester is the opportunity to do a placement year. It's a fantastic way to gain the skills and experience that graduate employers want to see, and it really will make you more employable.
League tables are one of those things that should be used with extreme caution - there's a good bit of info here on what they do and don't show
http://www.thestudentroom.co.uk/showthread.php?t=1096372 Whilst I can't claim to be familiar with Birmingham's Business School, I do know that Manchester's is very highly regarded.
Are there any activities that you take part in on an extra curricular basis, or anything you might like to get involved with at uni? It might be that one uni / city has the facilities for it whereas the other doesn't, which could sway your decision.
Have you visited both unis?