To translate from some of the above answers: The projected career paths of a mechanical engineering BSE from an ABET-accredited engineering program and a UChicago molecular engineering SB are very different. There is certainly some potential overlap if you look out 15-20 years into the future, but very, very little immediately following college graduation.
A BSE degree in mechanical engineering from an ABET-accredited engineering program qualifies you to be hired as an engineer by any of the hundreds of thousands of firms that employ millions of mechanical engineers world-wide. When you graduate, that’s almost certainly what you will do, at least for several years and probably more: work as an engineer for an engineering firm. If you can make it through the undergraduate program, as a practical matter you are basically assured of being able to get a job as an engineer somewhere, although the economy and your personal qualities and preferences may affect how many offers you can get and how good your pay and working conditions will be.
A molecular engineering degree from Chicago will not qualify you for employment as an engineer anywhere. You will be excluded from that market altogether, absent further education, and realistically, you are unlikely ever to work as an accredited engineer at a firm that does the sort of work accredited engineers do. You will be amply qualified to get admission to a PhD program, which may or may not be an engineering PhD, and which will put you in a position to do exciting, groundbreaking research in industry and academia some years in the future. That further education won’t cost you anything out-of-pocket, but it will defer fully reaping the rewards of your education.
It may also qualify you, depending on what else you have learned and what kind of person you are, to work in the financial/investment or business consulting worlds. There, you can get very well paid for being really smart and analytical, working very hard, and having enough basic knowledge in a tech field to understand the research other people are doing. You could also work in journalism covering such research and the businesses it spawns, possibly in sales for some of those businesses, or in government where they are regulated and often funded. You might work as a low-paid lab assistant for a year or two while you were deciding on or jumping through the hoops required to take your next step.
Or you may do something completely different. People who are really smart and who complete STEM degrees at elite universities like the University of Chicago don’t have trouble getting employed somewhere at a living wage unless they have overwhelming personal problems, because there are not enough people like that in the world and they are valuable. You might wind up as a lawyer, a doctor, an entrepreneur. But you will not have the neatly defined job market you can fit right into with hardly any friction or uncertainty that an actual BSE would provide.
By the way, if you had the BSE degree, you could probably do many/most of the things you might do with the molecular engineering degree, at least eventually, but you would have to swim against a pretty strong tide.
If you want to work as a professional engineer, there’s no substitute for a professional engineering degree. If you don’t want to work as a professional engineer, not being a professional engineer is a more direct route to achieving your goal.