The degree title matters less than the recruiting access and the story it creates for you. A strong MiM can be excellent because many programs are designed for early-career business recruiting, but finance, economics, analytics, and other Master's programs can also work well.
Look at whether MBB firms actually recruit from the program, whether students enter consulting at the level you want, and whether the timing of recruiting fits your graduation date. Those practical details matter much more than whether the program sounds more ‘consulting-oriented.’
You should also think about what skills the degree adds to your profile. A program that strengthens a real weakness or gives you a clearer career story can be more valuable than choosing a generic business degree purely for recruiting.
If consulting is the main objective, compare programs using actual placement outcomes and alumni paths. That will tell you whether the route works in practice. A useful reference is a Master's-to-consulting recruiting roadmap.