It's difficult to make a call based on the title of a degree. These could mean very different things at different schools. So at the risk of stating the obvious, you really have to look through the details of each program to get an idea of what skills and knowledge base the each program is set up to develop.
The biomedical engineers that I know essentially went though an electrical stream and then specialized on the biomedical side of things either as a senior undergrad or once they got to graduate school. So *they* would have been qualified for entry level electrical engineering positions, as well as BME positions when they got into the workforce. I'm not sure that's true of all BME programs though. I think some of them can be a little "fluffy" on the engineering side and leave graduates with fewer options once they graduate. So tell your son to have a look at where the graduates are ending up.
I think that biomedical science degrees tend to be a kind of pre-med, biochemistry mish-mash of stuff. For the students that do really well in them they're great. Those students go on to medical school or professional graduate programs in genetics, toxicology, clinical biochemistry, or rehab medicine such as physiotherapy, speech pathology, occupational therapy, etc. For the rest though, I think a lot of grads end up at the end of their fourth year trying to figure out what they can do for a career with a skill set that doesn't have a lot of demand outside of the healthcare avenues that require more training.