Europe (and to a lesser extent several Asian nations), have in de facto, practiced no integration attempts for their culture. Immigrants are fine. (legal anyways). This combined with a high rate OF immigration, and a low birthrate spells trouble.
Europe is not a single whole, and rates of assimilation vary widely, between countries and within countries between different populations. In France, for instance, there's a very high rate of shift towards the French language and a secular lifestyle; it's only a minority who stand out.
Official != reality. And note you linked the controversy, pointing out. Korea, per articles I did research on, changed their laws (so did Japan, too) vis a vis immigration, rather recently, in some ways, in response to the demographic curves. I suspect backlash they didn't expect is going to hit, and hit hard.
If that backlash hits, we can indeed say that conditions in South Korea re: immigration and integration are comparable to those in Japan. Until it does, we cannot.
Since they have since 2009 (IIRC): Where are they? I think you also forgot to factor in each nations' reputation there...
Reputations for what?
Different economic situations, too. Korea didn't have the same recessions, and same response to them. Apples and peaches, apples and peaches, there.
It actually is not. South Korea included members of the Korean diaspora as provisional members of the nation despite all the problems of integration and the wider society; Japan sought to actively exclude members of the Japanese diaspora despite same.