Faculty-wise it's probably not very different between NUS and Australia (I'll assume NUS is superior to NTU). Just like London. You'll get a lot of Asian (Chinese) lecturers and tutors just because they are studying/have studied at the same university you are at, then some of the local/regional variety (i.e. Australians and New Zealanders in Australia, Britons and Europeans in London, Singaporeans and other non-Chinese Asians in Singapore).

NUS and ANU already have a joint honours (Actuarial and Economics) 4 year degree (partly done at NUS and partly at ANU) which belongs to the Business (Commerce) and Economics faculty. So you can assume the two are comparable. Notable business faculties in Australia are probably Melbourne University, UNSW, and Sydney University.

Ranking wise, I don't think they hold a lot of credibility for undergraduates and/or for Business or Economics-type subjects, but NUS and Melbourne come pretty high and pretty close.

If you see Australia as a Western option, wanting to distance yourself from the same old Asian teachers (people from China, Hong Kong, India, Singapore etc), don't expect too much. First, you will likely get a large number of Asian teachers (they seem to fancy Accounting, Finance, Actuarial Studies, Statistics, Economics, and similar disciplines). Second, even if Australians have great English, some can be incredibly boring.

Choose Singapore, Melbourne, or maybe Sydney, and you have "lifestyle" I guess.

In Australia they'll probably prefer Australian.

Economics does not belong to Commerce, so BComm doesn't make sense. Economics also does not belong to Actuarial, so BAct also won't fit.

The title of the degree probably doesn't matter very much, except that some people in industry (depends what, where, who) are ignorant. Some people have no idea what Actuarial Science is and you have to explain it to them. The B Social Sciences degree with joint Honours is probably more confusing, as you can imagine.

This degree is not like a lot of other programmes where 2 degrees are awarded. This is a single degree. But it's unique in that you attend 2 schools. It's probably also hard. A single degree that takes 4 years awards Honours in either Actuarial Science or Economics. A double degree that takes 4 years does not award Honours in either.