Either is fine, they are abang, adik, well ...
In term of research, I would say NTU has the upper hand. I do hear news from NTU churning out profound innovations (recent one: the autonomous bus), not much from NUS (I could have missed them though).
For postgraduate, don't worry much. You may end up working in both universities. They have recently initiated a lateral exchange program, well, students are allowed to take courses from either universities, so, you're not confined to a single university anymore. I believe it's the same for research projects, usually both universities tend to collaborate.
NUS is at kent ridge (closer to town), NTU at pioneer (kinna ulu). If you're gonna stay in the campus, either is fine.
NUS evokes a quaint representation of a university, NTU on the other hand, slightly modern-like.
Decision is yours, if i were in your shoes, I would straddle too.
NUS or NTU?, Need suggestions/opinions of sifus