You'd be better off catching the subway (MRT) ... it's really cheap and fast. Unless you're earning huge bucks in Sing
As for Shanghai ... it's much, much cheaper to live there ... but the public transport if mainly taxis ... although it's also much cheaper to buy / lease a car and cheaper to park etc.
Singapore is basically like living in a first world nation ... everything is great -- health, food, schools, transport, shopping etc.
Shanghai is more like a developing nation. Don't get me wrong ... if you've got the money to spend then you can buy the best of health, food, schools, transport, shopping etc ... but if you're on an average wage / lower wage then you're more likely to live like the locals.
If you want adventure and the opportunity to maybe make a killing in development / business etc then Shanghai is the place ...
If you're looking for an easy life and have a young family then I'd go to Singapore
Cheers