<p>The two majors sound similar but are completely different.
Biomedical engineering is concentrated on studying math, mechanics, electric circuits, and computer programming in the goal of making medical devices that interface with the body. It is heavily math-based: a lot of your classes like biomechanics, biofluid dynamics, and biological thermodynamics will involve deriving purely theoretical, mathematical equations and then mapping these back on to a biological situation (I should add that there is a priori nothing uniquely biological about the math you learn - you could very easily apply the same equations to a trusses, pipes, power plants, etc.)</p>
<p>In contrast, there is much less math involved in Biochemistry and Molecular biology. It is the study of the molecular processes of life. Yes, this involves a bit of chemistry but it is mostly about understanding processes - enzyme A converts compound Y to Z, compound B turns on gene C which makes protein D which gets exported and binds to compound E, etc.</p>
<p>Freshman engineers will need to take more stringent courses than their science counterparts. I would advise you to take the harder courses that engineers take. It's always much easier to transfer from engineering to science than the other way around. Also, you probably won't actually do any engineering your freshman year, so don't get discouraged if the courses are too science-y or theoretical.</p>
<p>I started out in biomedical engineering but switched to molecular & cell biology. I was more interested in research and biochemistry rather than design and physics/electronics. This has been wonderful for me and I have no regrets about switching, but realize that the job prospects are much better for BMEs. You'll definitely want to get an M.S. in either field, but you might be able to get a job with a B.S. in BMEN, whereas just a B.S. in molecular biology is next to worthless. Definitely plan on going to med, grad, or law school if you do the biology route.</p>