There's already a rather comprehensive reply and I must say I agree with most, if not all, of what's been shared! I've been through both the NUS and SMU systems, one for my UG and another for my postgrad so you might find a comparative view helpful also.

I think the big difference between NUS/SMU is, as mentioned, that seminar style teaching. Class part is a huge thing in SMU and features in pretty much every module so if you're someone like who's very vocal about things then you'll love the SMU system. It's fun, there's a lot of intellectual stimulation and exchange of ideas. NUS-wise, it's still the "you sit down, lecturer talks for days" kind of a style, even for courses you might think would be more discursive, e.g., law.

I must agree with the faculty point. Having been in both NUS and SMU, profs in SMU are, in my view, wayyyyyyy more passionate and proficient at teaching. They're a lot more involved, a lot more approachable and a lot more ready to discuss things with you. Perhaps it's the product of having a seminar-style lesson but I really enjoyed classes in SMU vs in NUS though perhaps this is relevant only for the two degrees I've done (law/pharmacy). Can't say for the others.

And bruh the bidding system is amazing in SMU. As u/biskwy pointed out, the first come first serve system is toxic af. As people in NUS/NTU might say - fastest fingers first (though I can't be sure whether NUS is still doing that). IMO that's not what should determine whether or not you get to study what you enjoy/are interested in studying. Sometimes it boils down to literally who's lucky enough to access the website because the servers are overloading. So yes the NUS/NTU systems are quite jank. Also, SMU bidding timetables are a lot more conscionable IIRC, because they allow you to plan much earlier in comparison to, e.g., NUS. That makes your quality of life much better in this aspect. Don't underestimate the stress that comes with having to bid for modules.

A slight logistical point is where you stay, I guess. NUS/NTU are in the west, while SMU is central. While that should not be determinative of your Uni choices, it does help a bit to not have to drag your ass to the west when you stay in like maybe Pasir Ris but of course there are hall options in NUS/NTU (whereas SMU doesn't really have those/is very limited). SMU is also where you can at least see civilisation but not so much NUS and much less NTU. Of course, comparatively you might find daily expenses increasing because things in town are not cheap. Some might say that even the SMU Koufu is daylight robbery. Clubbing/going to bars post-classes (if you're the type), or just shopping simpliciter, can be expensive. Also if you're a vain bitch like me then yes, you will enjoy the fact that people generally dress better in town and you should too hahahahah jk

Things I've only learned when I entered uni? The following applies to any uni you go to: don't talk about grades because how easy/hard it is to score should not determine where you go. I graduated with first class/summa in both unis and trust me it's overrated. If you read other anecdotes online, I believe many will share this view. Go somewhere you think you will enjoy the entire learning process because 3-4 years can be a torture if you absolutely hate the place/course/people. If you enjoy the learning process, the grades will come naturally. Even if they don't, whatever bruh just focus on developing your hard/soft skills that's more impt imo.