
The question is do you want to measure Singapore by third-world standards or compare it to developed nations? Therefore I would leave simple geography out of it but rather look at the "league table" if you know what I mean.
For the same reason I wouldn't evaluate the level of safety in LA by anything lower than Western standards just because Mexico lies nearby...
Singapore does a great job at keeping crime low, no doubt about it. Not sure if draconian (albeit adequate) penalties are the sole reason, or if there's more to it. By Western standards (not just Western but developed nations in general) Singapore is probably 100x safer than most, but at the same time carries a 100x greater risk that you kid will get hit by a car so anyone new to Singapore should tell them to exercise extreme caution at all times (which should be done anyway, even in countries with extremely harsh road codes and low accident rates).

P.S. One a side note, I have never been to Jakarta, is it that bad? You mentioned Bangkok, have a friend who has lived there for almost 5 years, claims there is not a single part in the city where he would not go at any time of day or night. Loves it there but has since moved back to the US for a few years as part of his gov't job.