If it were me (purely personal opinion) I would definitely go UEA.
Birmingham is a massive medical school which may suit some but I think I'd feel a bit lost there, UEA has the perfect number of students in each year to make it sociable and personal: you could reasonably expect to get to know the majority of your year. Norwich is a fantastic city: as the county capital it has some prestige to it so shops, restaurants and facilities are very good plus Norfolk (esp. the North Norfolk coast) is absolutely stunning.
I'm not sure whether Birmingham use traditional or mixed teaching methods? PBL makes a huge amount of sense - learning in a small group environment is a quick and sociable way to start getting to know and work with your peers. It encourages teamwork, leadership, and self-directed learning plus it gives them an opportunity to keep a paternalistic eye on you and make sure you're not getting left behind.
No brainer I reckon (but it's not me going, it's you so what do you think?)...