If you meet the entry requirements for Birmingham definitely apply there, 20 isnt that old, people on gap years will be 19 so youre barely any different to them.
I think if you're commuting you will probably find it a bit more difficult to get the uni experience so you would probably have a better uni experience at Birmingham. The biggest advantage of Bmh is that its in a large city, so you've got lots of work experience and summer placement opportunities that have good links to the uni. Therefore getting experience may be easier.