Well, first of all, this is only MY opinion, I donīt work for any of these companies.

I listened in mono and used some spectra analizing and found that both keyboards use some sort of "fake" stereo. The sound (samples) could be recorded in stereo but use some extra processing for made it wider. The Yamaha effects are worse in mono, means also fake stereo processing. The korg isnīt so pronounced, just a bit less.
One thing that capture my eye and ear was the overall EQ: Assuming that both keyboards where recorded EQ flat, the yamaha has less power in the mid-highs translating in a sound similar to the "happy face" EQ. As the people increase bass and treble in their consoles the effect increases and thatīs probably contributing the weak yamaha sound in PAs (but also fake stereo and weak processors)
I think this explain why Yamaha keyboards sound so great at home: Theyīre mostly "tuned" for that. Korg synths sound appeal more to proīs
Conclusion: No keyboard is perfect. Choose what sounds best to you!
Best Regards
Jo Martins