It doesn't require much thought, its a fact - Birmingham
The reason being, the city of Manchester ISN'T that big, Manchester appear to want to add, Salford and all the other council areas to get their population figures - real population of Manchester is under half a million. These other areas include Bolton, Rochdale, Oldham etc etc and these are all towns in their own right, Salford is in fact another city. If Manchester can add up all those areas population then Birmingham can add the whole of the West Midlands conurbation, Its a close run thing but the population of the West Mids is still Greater than Greater Manchester