They are two amazing universities!!!! I will also be applying to both of these uni's for the same course so maybe I'm being a little biased
Bath's open day was great..... it really lived up to my expectations. Although it isn't a Russel group uni, it ranks 2nd for Psychology and has stellar national reputation in the UK.
Birmingham is another great uni that I will be visiting very soon.... I've heard many great things about the Psychology department which ranks 5th or 4th overall. Overall Birmingham for Psychology ranks 8th and it is a Russel group.
Both uni's are in the top 10 for Psy and have amazing graduate prospects, Btw what course will you be applying for at these unis? MSci or BSc or placement?