I graduated in science with majors in physics and mathematics/statistics.
Biomed/biochem is a common route to medicine. Sounds difficult and interesting from my outsider's perspective, but then physics and maths was difficult and interesting as well.
If you do science just make sure you do all the prereq's for medicine. I could apply to do medicine at Uni of Melb say, but I would have to do a biology/anatomy bridging course first as I haven't done bio since year 10.
A science degree covers a very broad range of disciplines, and you can generally specialise as much or as little as you like. Some units may be found difficult, some not as much etc. I don't know too much about biomed, but I guess looks like it is about biology + medicine.
I guess it comes down to what you like about medicine. If you are very keen on medicine and health I would think biomed would be better (biology + medicine). I would have a good explore of all the health-related careers out there. Personally I thought about doing a Master of Radiation Therapy which I could get into with a physics degree.
There are careers out there for people with a bachelor of science and nothing on top. If you think if medicine might not work out and you are interested in grad programs it may not matter too much what you actually studied, just that you have a degree from a university.
Hopefully someone from the biomed side can give their perspective. I can only really comment on this as a science grad who has thought about further study to get into a medical/health career.