Yup. This is business school ranking which is correct reference if you want to refer for MBA.

This and another list is the standard reference list. I forgot the name of the other list.

All sites have different methodology but FT is normally the go to to for MBA

Some sites such as FT and Economist don't differentiate by region

QS and Bloomberg recognize the the regional differences.

Generally, US MBA have higher recognition grade due to the employer's preference

Many factors but US syllabus tends to be more general than the UK/European counterpart. Normally require 2 years in the campus. Furthermore, US MNCs have more MBA related career program for MBA graduates. It's harder to find job in UK rather than US with the MBA.

Another important reason to study MBA is due to the networking opportunities. This is why London Business School is preferred over Oxford Said for example. I don't think people in London willing to take 1 hour plus train journey to Oxford to study.

For recommendation, follow the ranking.