Entry standards achieved for Medicine are about as high at Leicester as they are at Birmingham which, considering Birmingham is a slightly older university in a larger, more well known, city, shows how well regarded Leicester is for Medicine. According to The Complete University Guide, Leicester is joint 4th with Glasgow for research quality in Medicine (89%, ahead of Oxford on 88%), behind Cambridge, Imperial, and UCL. Birmingham is on 85%. Student satisfaction for Medicine at Leicester is first in the UK, on 84%, just ahead of St Andrews on 83%. Birmingham is on 72%.
To be fair, Edurank rates Birmingham as the 9th best Medical School in the UK and Leicester the 22nd. For context, they rate St Andrews 38th.
Topuniversities.com rates Birmingham 12th best for Medicine and Leicester 25th. For context, they rate St Andrews 35th.
I studied English at Leicester - loved the campus with its architectural contrasts - great students union - and the halls of residences give a very classic collegiate kind of feel.
But you should visit each place (e.g. university in general, department, accommodation) to see where you feel most comfortable. I feel that Leicester is good for those 3 things. For city itself, Birmingham has much more of a centre.