1. Because of the fixed rate between HK$ and US$, there is not much difference in using these 2 currencies. But the exchange rate in Seoul is a little bit better than in HK and there are actual differences in exchanging these 2 currencies in Korea.
2. Banks in HK may not have a lot of KWon because Won is not so popular as US$, JPY, EUR etc.
3. In Korea, if you exchange $, HK$ is not so popular and bank will change HK$ to US$ first and then to KW. So, the rate is lower.
4. The exchnage rate at the counter/shop in Incheon Airport (before you leave the gate) is really low. DON'T change $ there. The rate is 10% lower than the rate in the city/Seoul.
5. You can exchange US$ in almost all banks in Seoul. There are HKSB and Standard Chartered Bank. You may also go in other Korean banks and exchange money using your passport.
6. You can only change HK$ in some Korean banks which are authorized to trade in foreign currencies. So HK$ is almost no use.
It depends on how much you will use in Korea.
If the amount is small or if you are in a tour, change it in HK. No need to spend time in exchanging $. And you probably wont have time if you are in a tour.
If the amount is large or you couldnt estimate the amount that you may use, just take US$ with you. If there is any money left after the trip, you may change it back to HK$ with almost no loss in exchange. If you take KW back, you may suffer loss or have gain in exchange, depends on your luck.