These are both among the top 10% of UK universities. Your people are thinking about the undergraduate reputation of Durham. Durham is an older, snobby university, a sort of runners-up Oxbridge, while Warwick and Bath are the outstanding post-WW2 universities that are solidly in that top tier. A useful guide is:
https://www.thecompleteuniversityguide.co.uk/league-tables/rankings/business-and-management-studies However, you are not an undergraduate replying on brand equity of the university. You are an MBA candidate, and your placement will reply on the school's connections with mainstream MBA employers (whom most MBA students target) and the career and alumni resources. 96% of Warwick MBAs were placed withing 3 months, in the last FT ranking, compared to 73% of Durham MBAs. Warwick MBA students earn more on the way in (more senior cohort) and more on the way out of their MBAs. They are much more highly recommended by MBA alumni of other schools. Their career services are very much better. In an academic setting, the school is much. more highly respected for its research than Durham. It is much higher ranked for international mobility, and has much better gender balance, than Durham.