I have a biochemistry degree, and currently work as a chemist. Some of my coworkers have biology degrees. If you are a biology major with an emphasis in biochemistry, you will take a lot of the same classes as a biochemistry major, so will be pretty much equal for applying for jobs. For me, I had to take physical chemistry and bio majors didn’t have to, so that is probably the only area where I would have an advantage over a bio major.

I may be biased as someone with a degree in biochemistry, but I think that’s a better route for medical school. In a traditional curriculum, you’re going to start out with something like biochemistry and anatomy, and it’s a little less stress if you already know most of the biochemistry (a medical school course can be a bit different in content than an undergraduate course though). Then, biochemistry is fundamentally important to understanding a lot of the basic sciences taught in medical school. It’s a big part of microbiology and of pharmacology, for example. And yes, you might have slightly better career options with a biochemistry degree. If you wanted to go to grad school in a biomedical science, you’d have a leg up in the application process as well as in understanding the first year’s curriculum. If you wanted to just go work in a lab, the jobs are at medical schools or pharmaceutical companies, where biochemistry is more important than ecology or whatever else you might study as a biology major.