U go Melbourne you full fee paying.
U go smu, you are a subsidised sinkie.

As the saying goes, money is king. The aussie univs needs your cash
For eg very hard to get to nus medicine or smu law but walk in the park for aussie unis.

As such employer knows, the calibre of sinkie locals that graduated from local univs vs local sinkie that grad from aussie

However, for a native aussie, it is hard to get in, as they are subsidised.
Smu or nus is virtually unheard of in aussie, umel is perceived as low quality in singapore.

So it depends where u want to work next time