Well, besides the minor point where Stanford isn't an Ivy League uni, admission statistics for top tier uni's undergraduate are always worse (ie lower acceptance %) compared to their
MSc programs (see link for the Stanford MSc's admission statistics). I agree that statistics for MBAs, MDs, JDs may be even worse than undergrads admission and that most MScs are cash cows for all universities since they usually do not provide financial aid to MSc students. Unfortunately I can't turn back time and choose to go to a more prestigious university than NUS for my undergraduate, so the comparison between a MSc and undergraduate education at a top tier university is pointless.
So that brings us to a comparison between the Stanford MSc, or a local part-time MBA (NUS/NTU/SMU) (Feel free to provide more pro local MBAs argument since you didn't exactly mention why you think the local MBA option is better).
Since my employer will only pay for a part-time or distance learning masters, there isn't many other options available unless I want to fork out the 60~100k (not counting opportunity cost and living expenses of 100-200k) out of my own pocket for a full time program. Hence cost is not a concern for the comparison between the MSc and the part-time MBA. GMAT (740) or GRE (162V/170Q) is also not a limiting factor.
I applied for the
Stanford MSc (see link for more info if interested) via their Honors Cooperative Program (HCP), which is a part-time/distance learning option for students working at some companies. For students in the bay area/palo alto (this comprise the majority of the HCP students), they can attend the lectures in person (or watch the recording online), and they will have to take the exams together with the full time student on-campus (students further away requires a proctor for invigilation). HCP students and full-time students do take the modules at the same time, and are graded upon the same criteria. Does this make the MSc an online degree other than the factor that I plan to complete most of the courses online as compared to a degree that's offered fully online (eg. Northwestern's online MPP) without a brick and mortar equivalent?
My concern for taking the MSc mostly via distance learning is mainly the loss of the networking with professors and other students as compared to taking a local part-time MBA. I guess in my decision analysis, this loss of networking is something I find difficult to "price" appropriately. Not being on campus also limits the cross faculty modules available (eg won't have access to Stanford GSB's modules), and lack of access to campus recruiting. If I do take up this MSc, I do plan to do one to two quarters at palo alto while working remotely (my work is somewhat flexible, and only requires my laptop and an internet connection), though it is still far from a perfect solution to the loss of networking.
Hence I am
still considering the pros and cons of the MSc and the local part-time MBA

Opinions are welcomed, and may help in influencing how I "price" in the cons of doing the MSc through distance learning despite the brand name.
It is conducted in Palo Alto, though I plan to complete most modules via distance learning while spending 1-2 quarters at Palo Alto. I also have the choice to convert to the full-time program if I am willing to pay for the tuition fee (~60k sgd) and living expenses (~20-30k sgd) out of pocket though.