While I don't usually take cabs in Japan, my school has sponsored three days worth of cabs in Japan which my class gratefully accepted. I have summed up my experience over these three days, and will be using that as a comparison with Singapore's cabs.
Do note that it might make your trust in Singapore cabs fall a little but at the end of the day, I hope we can all appreciate cabs in Singapore and their drivers better!
Cabs in Japan take courtesy very seriously and this is evident from how they treat their passengers. In Singapore, we might come across situations where taxi drivers do not open the door for us when we are about to board but this is almost unheard of in Japan.
Most of the drivers greeted me upon boarding as well. And to take things a step further, they are well-dressed in suits, and this sets them apart from Singapore in the sense that you feel like you are on a V.I.P car even though it is one of the cheaper ones available.
In the same way, Japanese tend to fill up the back seat before the front and you wouldn't exactly board a cab in Japan in the front seat.
2. Trust and Security
Trust is very important between driver and passenger, especially if you are a lone female taking a cab late at night. I'm sure we have all been warned against that at least once.
In Japan, cab drivers have their particulars on the windscreen...
or at the back of the seat.
In the same way, drivers have a huge translucent tinted board behind them and this keeps them safe (to an extent) in cases when passengers attack the driver.
As for traffic security, most drivers refuse to accept more than 4 passengers per cab, which is a far cry from the slightly more casual and flexible Singapore cab drivers, who may go for more personal small talk and may also allow squeezing to fit more people on board.
Needless to say, Japan's cab prices are more steep. It is easily twice or thrice of Singapore's prices and that gets even steeper at night. Each trip I took in Japan for about 20 minutes were 3000 to 5000 yen, excluding surcharges -- a rather steep rate that I have yet to witness in Singapore yet.
Singapore or Japan? Hard to say, but as long as I'm deep in figure collecting, I'll choose the cheaper Singapore fare any day!