Well, I'm currently in the process of studying for a BSc/BA at USyd... I can comment on it, but not on the one offered at UNSW (apart from the 4 year duration, I think?).
It is very broad, so there is no doubt that your units of study would vary to mine and that you would see the double combination under a different light.
I am currently trying to determine whether I stay for the entire double, or whether I just see if my marks will be accepted for an honours year in the BSc (so far they easily make the grade, but who knows). The degree combination seemed like a great choice at first, with being able to study a science for a career and an arts unit for the sake of learning, but then after some time I realised that I was merely continuing on with what I was doing at school (cruising along without a great deal of effort), and that 5 years is much longer than I first expected, and that I really wanted to wok as soon as possible. I also flirted with the Bachelor of Economic and Social Science degree for some time, too.
Not noting the difference between Table A and Table B majors in the BA until part of the way through first year has played a major role in these considerations (I thought that I could easily take a government major if history was not as interesting as it seemed, however, while possible, it would mean that I would have to sacrifice a science unit or two) .
Most of that is useless, but it may help you in showing that 5 years is a long time. I do enjoy it, and at least you have the option of continuing on with or dropping the BA at the completion of your BSc (with your preferences being dominated by sciences I would assume that the BSc is the more important of the two). Taking a joint honours year for the two degrees is another great option, too.
Two points of actual value:
1. Note that in the BSc/BA your Table B options for the BA are limited.
2. Don't listen to people who tell you that there is no point in continuing on with the second and third years of the BA after the completion of the BSc, as it can really annoy you when you start to adopt that view at the expense of your original aim.
That must be one of my longest posts... With most of it being a personal rant... Fwoa!