More to add to this.
There are several fields of study where going local and overseas do not matter. There are law, medicine and dentistry.
I am quite sure an NUS law grad does not command lower pay substantially than a law grad from Oxford, though the latter has a branded degree. If the former is on the dean's list, his starting pay is higher than his peers who are not substantially and also will be higher than an Oxford grad not on dean's list!
Medicine graduates as well. If i'm not wrong however, foreign medicine graduates did not enjoy the government subsidy, and can move to private practice earlier than local medicine graduates. This is how they can get higher salaries. However a foreign medicine graduate who chooses to stay in the public sector will not command a higher pay than a local medicine graduate that chooses the same.
The brand of the degree REALLY matters a lot more if you're talking about general degrees. That's when the difference is pronounced.
For eg an Oxford PPE graduate has many more open doors and easily commands a much higher salary and has job offers from top banks and consultancies than a local NUS FASS grad can only dream of.
Other courses of study like engineering, general science (physics, chemistry, etc) and Mathematics, a branded degree opens more doors and in higher places than local one. Why? Because for these courses, the brand really matters since the course is not (as) specialised. Engineering graduates from IC and Cambridge can apply and get job offers from top banks and consultancies, which local engineering grads do not. Same for the other courses. I know a couple of investment bankers who got Maths degree from IC, and analysts and consultants who got Sci/Engin degree from IC/Oxbridge/IvyLeague/MIT. Local grads from these disciplines do not get the same opportunities as them.
This is where the course you choose matters. So if you're doing medicine or law, it's better to do local and can save more money, unless you are willing to pay a premium for the overseas undergrad experience.
Mingling with the people in top overseas universities, who may be heirs of huge empires and princes of royal families and having a nobel laureate as your lecturer are just some of the benefits you pay for shelling out so much more money to go abroad.