Hey OP! I'm doing both a BBiomedSc and a BSc, so I hope I can give you some good insight into both of them.
The primary difference that I've noticed between the two (offered at Monash) is the degree of breadth and variability in study available. Biomed is a very set, straightforward unit - it consists of a series of "core units" that you take over the course of the degree, usually three per semester (assuming a full-time study load and not doing a double degree). As I mentioned, it's a very straightforward, uncomplicated pathway; for people doing single degree biomed (or biomed advanced with honours), your first semester will be BMS1011 (Biomedical Chemistry) + 1021 (Cells, Tissues and Organelles) + 1031 (Medical Biophysics) + one elective from pretty much anything you like.
If you're doing a biomed double degree, it gets a little more complicated. Generally, it's fine if you're doing a double with Law or Arts or Commerce etc, but there are a couple of issues with Biomed/Science or Biomed/Engineering - this is simply because some of the biomed core units may be prohibited by some sci/eng units, or vice-versa. An example of this is that I could not take BMS1021 for biomed because it was prohibited by BIO1011 (Biology I) as part of my BSc. In the event of this happening, you simply need to make up for the missed credit points with an elective from the biomed faculty (Medicine, Nursing and Health Sciences). It gets a bit easier in later years, as one biomed unit can take the place of two regular science units that you may otherwise need to take for a BSc major sequence (as with a Genetics major, for example).
The Bachelor of Science, in contrast to the Bachelor of Biomedical Science, is super flexible. You can pursue any particular area (or two) that takes your fancy. You can certainly cover all (or almost all) the biomed course material through a BSc, but through biomed I find that it's a lot more focused, and you'll often cover two science unit's worth in one biomed unit (such is the course structure). I personally advocate the double biomed/sci degree for those who are interested in other areas of science beside that of a biological nature - but in all fairness, I'm pretty biased

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At Monash, I haven't noticed any disparity in "prestige" between the two courses - you use many of the same labs and facilities depending on your classes, and you're essentially always just as employable with a BSc as with a BBiomedSc.
Going on from this, I'll just try to discuss some pathways post-biomed and post-science. Biomed is seen by some as a way of obtaining entry into post-grad Med - one of my friends has described biomed as an 'extended GAMSAT prep course' (personally I don't agree with them, but it's a funny little anecdote!). Biomed also leads into a number of specialised research positions (an example can be seen through the Medicine, Nursing and Health Sciences section
here). It also allows for the formation of somewhat closer ties with certain staff who may supervise you if you go on to do honours or post-grad stuff.
Science offers most of these same opportunities, and again, it's flexibility as a degree means you can do so in whatever you want.
And just to address your last point:
If I want to do.. only up to bachelor degree, should I choose science instead of biomed?
but then if I get high enough score to get into biomed... wouldn't the score go to waste if I don't put biomed on top of science..? 
There's no such thing as "wasting a score" for entry to university - you should do what you
want to do, not what your score dictates you should do. For example, my cousin was doing physiotherapy at La Trobe - her parents convinced her to take it because she had a high ENTER (this was back in '09), even though she wasn't really interested. She's just moved to Monash to do an Arts degree, and she's enjoying it a lot more.
If you'd rather do science, put it on top of biomed. If you'd rather do biomed, put it above science. Don't let your score force you into a course if you'd rather be doing another - there's not enough difference between biomed and science to justify doing this.
Sorry I'm a bit late to the party, but I hope I gave you a semi-good insight into Monash biomed and science. I'd be happy to answer any further questions wither through PM or in this thread
