As a graduate of both, I don't think there are any business school rankings that put Edinburgh above Manchester.  

I'd taken a look at some rankings such as this one:
https://www.study.eu/article/top-10-best-business-schools-in-the-uk
This one does place Edinburgh above Manchester (not in the top ranking, which is just business schools, but in the one underneath, which ranks MBA programmes).

That's not a 'live' ranking. It's a table of schools, showing the percentage increase in salaries. The data come from The Economist, which exited the ranking business and was widely pilloried for its ridiculous methods. That favours schools whose students had limited experience on the way in. 

I was completely unaware of this. Thanks for shedding some light on it. Won't be taking those rankings seriously anymore, and for sure will be taking The Economist with a pinch of salt.

The Economist is an excellent "newspaper" (as they call themselves) but it's hard to find an original angle on rankings. They experimented with rewarding schools with high increases, but that pulls forward schools with less experienced cohorts that had higher growth (Fudan, Georgia, Northeastern, UMass, etc) and pushed down schools with higher quality cohorts (Harvard, Insead, Stanford, Chicago etc) even though those MBAs have much better outcomes.