I’ve lived in all three, too, so maybe I can chime in here.
Korea:
Like others have already mentioned, the food is pretty much all the same, smothered in gochu jang, dull or just really weird. As for the people, I’ve never met a more miserable and xenophobic lot - seriously, the uber-nationalism one has to endure there on a daily basis is just too much. And for a city the size of Seoul, finding decent western/ethnic food there is difficult and way over-priced.
China:
Well, it depends where in China you are. I’m currently in Nanjing, which is a great city - it’s safe, the people are generally friendly, there are great food options, both western and local, it’s close to Suzhou and Shanghai (although why anyone would like Shanghai is beyond me). If, however, you find yourself in small town China, or crappy cities like Changzhou or Taiyuan, you’re in for a world of hurt. Endless hellos, peasants bugging you for cash - I think you get the picture.
Good second-tier cities for living in China are Nanjing, Suzhou, Chengdu, Dalian, Kunming and Hangzhou. Not too sure about places like Shenzhen or Guangzhou as I have yet to check out Guangdong Province.
Taiwan:
I liked Taiwan. I think the mainland has better Chinese food options though. Also, the Mandarin in China is better - Taiwanese use more tones, for example peng(2)you(3) in Taiwan becomes peng(2)you in China, dou(4)fu(3) - dou(4)fu, xie(4)xie(4) - xie(4)xie, and so on. Simplified characters are a heck of a lot easier to learn/read/write, so that’s an added bonus, too. Expect to be hot and sweaty most of the time in Taiwan, or soaking wet from the rain. Taiwanese people are friendly and laid-back I found.
Overall, after 2.5 years in Taiwan, 3 years in Korea, and 1.5 years in China, I’d say China is my favorite as the country is absolutely amazing to travel in, Taiwan is second, and Korea is last (and rightfully so).
With regards to money, making money in China is easier than you might think, and the cost of living is very affordable. The money was good in Korea and Taiwan, but in the case of Korea most of it was spent on alcohol just to try and remain sane in that place, in Taiwan a lot was spent on ladeeez.
OP, I’d definitely choose Taiwan over Korea, and the won is sucking monkey balls now next to the dollah.