Well I can't answer the UNSW side of your question much, but I'll try with the UTS side.
Basically, the BBusiness has more core subjects in the first year than the BComm or the BEco does (as far as I know). These core subjects are all required if you're doing the Accounting major (so the BComm students end up doing it anyways), but if you're doing another major, then usually you wouldn't have do some of the first year subjects in the BComm, whereas you'll have to do them in the BBusiness. This isn't a bad thing though, as it's all general Business stuff that's relevant to most job fields.
As for between BBusiness and BEconomics, well I think the economics degree is focused towards economics, so if you want to go into that field, then that course is good for you. As far as I know, it's just a more focused BComm degree, in which you can still do a 2nd major if you want.
As you already know, you can do 2 majors in the BBusiness (so like Accounting and Economics), if you want, though only 1 major is mandatory. The other can be made up of a sub-major and electives if you wish.
Now, all the BBusiness combined degrees only have 1 major, because you are already focusing in another area in the other side of your combined degree, so to make sure you're not spending 5-6 years at uni, they cut out one of the majors. You'll find this is pretty standard across most uni's. So basically, you usually do one Business major and then one major from the other side of your degree (whether your doing IT, Science, Engineering or Law).
As for choosing the BBusiness/BComputing course, I would only choose it if you were interested in a career in an Information Technology related field or in a field which requires both, and you have an interest in computers. As with any IT course, the content can be fairly technical, and so you need to have an interest in it to enjoy the course and do well at it. The course content isn't too hard, in my opinion, and most students get through the IT courses without too much trouble, but that's because they are interested in IT. The BComputing side of the degree will allow you to do a sub-major in an area of IT you're interested in, so you'll graduate with a combined degree with 1 major and 1 sub-major, in 4 years.
If you choose to do the single BBusiness degree, you can just do a 2nd major in IT, but in my opinion, you may as well spend an extra year and get a 2nd degree, as it's a lot more beneficial and will be more recognised by employers.
Hope this helps.