In essence it is up to you. I go Sheffield and absolutely love it! I've secured a TC at a MC firm, so as long as you work hard there is no reason why you shouldn't be able to do the same. Saying that, I am sure there are plenty of people from Birmingham who have done the same and if you asked they would say they loved their time there.
One of my friends did go to Birmingham for a year and then he dropped out because he just didn't like it. Despite living in Birmingham before, he didn't like the location of where he was or just the vibe and culture of the place (obviously he thought he did from the open day though). He then moved to Sheffield and couldn't happier.
Personally I would say Sheffield, however, neither will really put you at an advantage of disadvantage compared to the other so it is very much where you think you will be happier.