Studying in public university is always a better option.
NTU is recognised worldwide (atleast it is in top 100).
If you concern is about earning money, which is for most of us, the decision will be dependent on what salary makes you contended. For me, I am happy to get 6k and live the life I want.
Engineering sector is generally a low paid sector here in SG (so many engineers out there). You can read in the threads too that it takes a lot of years for the salary to increase. In Singapore, if you want to earn, you have to be your own boss (real estates, trading, consultations etc.). Expats are paid a high salary in engineering sector (foreign talent), and for that matter in any other sector.
Many of my friends who had completed Engineering from
NUS and
NTU did not join engineering sector but had joined banking due to its lucarative pay. It is well known - An engineer can do anything - that is true as Engineering Degree will force you to study almost all subjects (we had studied modules related to LAW, HR, Programming, Business, History etc. etc. etc.) In a way, your employability is improved/increased. With a Banking Degee you cannot work as an engineer, but with an Engineering Degree you can be hired in a Bank.
Pvt. vs. Public university -
If you wish to be in academia or join as Civil/Public Servant - study in a public university. Everyone has their own opinion, but it is well known in the academia, a student from a public university is better off compared to a student from private university. The general feeling for a pvt. degree holder is - pay money, get degree.
Later on in your life, if you wish to work as a Civil Servant (and trust me it is a good option), you will regret taking a degree from private university. Your chances of being hired will be considerably reduced. Even if you get a 1st class honours in Pvt Uni, compared to 2nd Upper in
NTU, a
NTU student will be hired for the job. But, if you have decided that you will only be working in the industry - then a private degree is fine. They geneally don't care about grades.