Wellcome Jens,
I was a Korg utilizer for about 20 years, and initially I was missing many Korg styles.
Then I gradually discovered that the Yamaha world offers a huge quantity of Styles additional to the ones preloaded. This means that you can cover any song of any genre you like to play.
In this Forum, in the Styles section, you will find hundreds and thousands of Styles. Download, listen, select and save what you like/need. That's it. And for free!
You will also find some Korg Styles conversion. But normally they are very far from the originals, and sometimes not even playable. That's because Korg Style structure is TOTALLY different.
But you will do well with the Yamaha additional Styles.
The best of them are often the ones made with the SFF2 system. They can be used in arrangers from Tyros3 on, and PSR S610 on (not PSR S900 which is older). But I understand that you have a Genos = no problems at all.
Ciao,
Angelo