Hi Abby,
Thanks for your question!
There are a few key differences between the Big 4 (KPMG, EY, Deloitte, PwC) and MBB.
Nature of the work - The Big 4 are traditionally accounting firms, which now provide a wide range of professional services including audit, financial advisory, tax, legal and consulting. The Big 4 and MBB may work on similar types of consulting projects, but it will depend a lot on which office you work for, and which practice area you end up in. Historically, the Big 4 have had a bigger focus on operations and implementation, whereas MBB have focused more on pure strategy questions.
Hours worked - As a junior in a large professional services firm (i.e. Big 4 or MBB) you can expect to work 60+ hours per week. In other words, Big 4 and MBB will both be long work hours. This may vary depending on what projects you are working on.
Prestige - MBB is much more highly regarded in the consulting industry. Why? Well, they spent many years and millions of dollars to make sure this is the case. MBB tends to attract higher calibre employees who studied at more prestigious schools, and as a result MBB consultants tend to progress in their careers much faster (whether it be promotions within MBB, heading off to B-school, or taking a job elsewhere). Don't underestimate the value of a powerful brand name.
The People - Most people who land jobs in consulting at the Big 4 and MBB will be smart, hard working and generally impressive individuals. That said, MBB has more pulling power, and will consistently attract the best of the best. Historically, MBB would only recruit from the very best universities, however it seems they now consider a broader range of applicants.
Exit Options - Big 4 and MBB will both offer you strong exit opportunities (e.g. B-school, industry, PE). In my experience, business schools and recruiters place a premium on MBB compared to Big 4. MBB are the Oxbridge of the consulting world.
Does that help?