For some tiers, drivers have to have 5-10 years of accident free driving - in Seoul that's remarkable.
Here's an example fare: $2.50 to pickup and go 2km, about $.70 a km after. Gangnam to Gyeongbokgung palace (across most of the city and over a major river) will run you about $15.
A trip from Brooklyn to Harlem, about the same distance and complexity, is likely to run $30-40. Uber will run you $40-50.
Here's a relatively good list of costs in Korea.
$1 ~ 1,000 Won.
For example, in London, Black Cabs are generally considered decent but expensive, so Uber is priced cheaper than black cabs, but slightly more expensive than mini cabs.
In Delhi, the prices are far higher than anything you can hail on the street, but cheaper than calling a town car service.
I'm not sure if anyone in Korea would pay the premiums that people pay in NYC/SF, especially if taxis get a comparable app.