Hey Chris,
Technically the Korean government requires teachers to have a degree for the purposes of processing a visa. However, (I haven't done this personally), some schools will turn a blind eye to teachers without a degree and you can get by on a tertiary qualification of some description. It is up to you if you want to risk it though.
You can make good money in China, generally they will pay your accommodation and if you work the full 12 months they will reimburse your flights too. My advice though is ALWAYS check out your schools as there are a lot that will try to scam you. Don't deal with recruitment companies either.
Best of luck