The incarceration rate is much lower. The US has an incarceration rate of 541 per 100k, Singapore is 178 per 100k. Singapore is just much more likely to execute convicts; in part because SG has a mandatory death penalty for some crimes, and in part because much of the US doesn’t have the death penalty in all.

It does not appear to be an effective deterrent. https://www.academia.sg/extra/death-penalty-research-appendi... This article has a criticism of the SG government report (Study 6 header) on the deterrent effect when they added the mandatory death penalty in the 90s. The big takeaway is that convictions didn’t drop notably (cannabis convictions dropped a single percentage point, opium convictions went up 2%. Average opium weight seized dropped a ton, but is still like 13 times the mandatory death penalty limit so hard to call it there).