I think pay at international schools in Thailand can be quite good ($40,000+), I had a friend who taught with his wife at a school in Bangkok (though not English language, the courses were taught in English).
Besides that though, generally the pay is a lot lower compared to Korea or Japan. Of course the cost of living is cheaper, but you won't be able to save much. The reason Korea has become the destination of choice is that the salary is close to Japan but the cost of living is lower, and Korea seems a little more westernized (and the english is better).
In Korean universities, the best jobs are those that pay $4000+ per month for 9-12 classroom hours a week, two fifteen-week semesters per year with paid vacation. But you generally need to have been in the system for a while and built up your CV, perhaps even have some relevant research experience. My job was with a university language institute, which usually incorporate the english, korean, and other minor language departments into one center. Some of these aren't much better than private institutes, but I was fortunate to work at a good one. Base pay (16 teaching hours per week, about 34-36 weeks per year) was about $2500 with free housing, but you get other bonuses and with a couple odd tasks my take-home pay averaged over $3000 per month, which is more than enough to live comfortably there.
Japanese universities are a different pony. Basically, they're more competitive, but if you end up landing a position you can be making $60k-$70k your first year. Never worked in Japan though so can't really comment on the culture.
I would definitely consider all options. Some people find Korea or Japan isn't their cup of tea and prefer the more relaxed southeast asian lifestyle. With Japan though, I think it's pretty necessary to learn the language (most foreigners I met there spoke japanese). People tend to be more transient in Korea, just spending a year or two there, and while it's definitely possible to learn the language to a good conversational level in a few months, for most people it's not worth the investment, as you'll meet enough Koreans with passable english to get by. Almost all my expat friends in Thailand speak thai fwiw, and although the script is much more challenging than korean, I don't think it poses as much of a challenge to an english speaker.
Anyway, as for myself I'm working a corporate job now that'll likely see me back out in asia fairly soon...leaning toward Korea, but considering Japan (though I'd have to learn Japanese) or other countries as well. Good luck.