Hmmm...no one has answered you so I will attempt to. From Busan, there is no easy way to get to either place and I suggest you go to Soraksan (Mt. Sorak) last, just for ease of travel....unless you intend to leave country via Busan. Or you should use Pyeongchang as a base to see Soraksan.
Either way, you can either use a combination of the train and bus to get there or just the bus alone. The train can only take you as far as Dongdae and you will have to switch trains in Gumi for Dongdae. You would then have to take a bus to the resort from Dongdae (very easy). So, you will need to figure out the best way for you to get to Dongdae from Busan based on your budget, the amount of time you have and your speaking ability with Korean.
Honestly, other than my suggestion, you could go to the Korean National Tourism Office in Busan and they can help you map out your travel plan for you. They will do this for free. Their location is in the link below:
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