|>> || I'll give every bit of advice I can, but my experience with Korean is mostly academic and impersonal. |
They have very... tense relations. Not that that should matter.
Both languages are drastically unlike French, Spanish, or German, though the phonologies and grammars are a little like the mixed.
They're at similar difficulty levels, though Korean is just a little harder. They have very similar grammars, similar phonotactics, and similar pitch/stress/timing patterns, but they have different phonologies; Japanese is like a simpler Spanish, but Korean has a lot more, including altaic vowels (an ö and ü broken into we and üi, an unrounded u, which to be fair is the default allophone of /u/ in Japanese). Japanese has a very rigid 5 vowel system, but Korean has a 7 vowel system where the near open vowels have slid to more close positions. Korean has 3 rows of stop consonants - ptk and bdg like us, but also a set of tense consonants in the places of ptk too where you tighten your throat. (graphically, <pp><tt><kk> and the non-stop <ss>; eg dal means moon, tal means mask, and ttal means daughter). Korean even has traces of vowel harmony, but that's simple enough.
Writing systems add a whole bunch of difficulty points back to Japan, evening things out. Korean uses an alphabet like ours, except the syllables are scrunched up into blocks. Chinese characters are used only very rarely now in SK, usually in scientific things to distinguish homographs (like boohoo tear and shred tear). There's usually 1:1 correspondence spelling wise; their alphabet, and thus their writing system, was historically put down but today championed as a writing system you could learn in a day.
Japan on the other hand uses a syllabary, where each "letter" represents one whole unique syllable (it's simpler phonology, though, means this isn't quite as crazy as it would be for English or even Korean). Except it doesn't just use one syllabary, it uses 2. And to top that off, it uses Chinese characters unsparingly, so you have to know those. There's some patterns you can gleam from the Chinese-derived pronunciations of the characters (oh yeah, there's usually two, often more pronunciations of the characters), but because Japan evolved independently, most of the characters have no patterns whatsoever to their pronunciations. You really have to suck it up and memorize.
Business wise, I think you could find a life either way. Though I do have a feeling that at least relatively speaking, weebs flooded the Japanese market, making Korean a superior choice. Japan's economy is staring down the barrel of gun too - its population is growing older, it suffers from an untapped workforce because men are expected to do things like 15 hour work days while women are expected to be stay at home, the people in charge are all really really old too so they're stubborn and uncompromising. But all of that's also true of South Korea, except they're riding the economic rollercoster Japan rode about 20 years behind. The major economic difference between the two will come whether or not the North falls; you really shouldn't bet on it, however.
Both Korea and Japan have very... well, I see it as phoney systems of politeness. Korea really stresses things from a Confucian POV and Japan really stresses things from a... well, Japanese POV. Japan's is like 100 times more intense, though - never ever insult your superiors unless they're not around. Don't make your "team" look bad, but be humble when its just yourself. I don't know. Korean is a lot like that, but much less "you're a white boy and don't know what you're doing but we're gonna think you're rude anyways". In my very very limited experience. What I'm more used to is Chinese good-natured bluntness, and I hear Koreans can be very blunt but I've not noticed it much. Again though, very very limited experience.
Politics and things people care about are... odd. Both have very conservative societies. Japan's left is louder than it's right but it's right is naturally older and thus more populous. Japanese people *really* hate koreans because of the zainichi population, but of course that roughly correlates to an individual's politics. Japan is a little more proud of its left, however.
Things in Korea are understandably batshit considering the other Korea. The country was a relatively brutal but efficient right wing dictatorship until the 90s, when it democratized. That really polarized the left, to the point where they romanticized North Korea. Now if you somehow became Korean and voted, you're torn between the Dictator's Daughter (the current president) and the North Korean apologists.
But you're really not going to vote in either country - both have a very ethnocentric view of citizenship and nationalism. Both are extremely homogenous to the point of xenophobia, though Japan's getting a little more violent as it struggles to adapt, since its starting to give a cm of ground on the issue. But if you make your opinions on things known, Koreans are a little more... unable to bring themselves to be friendly to those they strongly disagree with than the Japanese, though this is really not that major a thing.
Since both are very different than anything you've encountered, I suggest one at a time. Overall I recommend starting with Korean, and then picking up Japanese later, but by a hair's width; Korean has just a touch more potential, and it's slightly greater difficulty means that if you want to learn something later when you're busy you can put more your effort into vocab, idioms, and so on for japanese than learning abstract things like vowel harmony etc with Korean. Though Japanese is established, it actually has negative potential due to the economy.
You probably could do both though, but I wouldn't really want to risk mixing the two, or at least putting koreanisms into Japanese.