which hospital is the best for labour? Private or public hospital?

If high risk pregnancy, go to KKH or NUH. KKH has really experienced gynaes and nurses so you are in good hands. If you can afford, go for private as there's difference between the experience of private and subsidised. If you think you are a low risk pregnancy, then any hospital of your preference would be good! Ultimately, in the event of complications, just check yourself in to KKH cos the bill size would be significantly smaller than private hospitals.