According to Wikipedia:
MB ChB are used at the universities of Birmingham, Bristol, Leeds, Leicester, Liverpool, Keele, Manchester, Sheffield, and Warwick.
MB BS are used at the University of East Anglia, Hull York Medical School, Imperial College London, the University of London, and Newcastle University.
BM BCh are used at the University of Oxford.
BM BS are used at the University of Nottingham, Peninsula College of Medicine and Dentistry, and Brighton Sussex Medical School
BM is awarded at the University of Southampton.
MB BChir are awarded by the University of Cambridge.
They're all equal, obviously. Quite interesting!