Re: LSE or MBS for MBA ..!!
Rankings can be superficial thus exact rankings are difficult to calculate.
I think overall, Manchester is > Leicester. As a city, its bigger, more cosmopolitan and is truly a student city. Ahead of London. London is too big to have that student feel, and has loads of unis spread across the city.
Besides Manchester is making huge strides overall, its only a matter of time Manchester takes over majority of UK unis in quality and quantity. They’ve built like 10 new buildings which are forefront of research etc..
Besides Manchester United and Manchester City > Leicester City 
(this is coming from a Liverpool fan)