There is a pretty deep discussion on Korg Forums:

I have found the PA3X to have better operating features for real-time use. The operating system is pretty good, but there will be a learning curve coming from Yamaha. The Songbook feature is wonderful, and the ability to edit and change things is great, and easy.
Yamaha has those wonderful presets in the OTS for right-hand sounds. You can get good sounds from Korg too but you will have to dig around a little.
There is an update scheduled for June 1 that will make it even better.
Key size and feel are great on the PA3X. The Vocal Harmonizer is outstanding, far better than the Yamaha.
It's a little heavier than the PSR, but smaller, a little lighter, and far easier to carry than the Tyros.
You will have the ability to edit, delete, move and over-write all Factory styles on the Korg.
You CAN NOT audition styles from USB; they have to be loaded into the User or Favorite Banks to try them. Not a big deal, but not as easy as Yamaha to try things out.
It has a Chord Sequencer that you might find useful for real-time looping.
It has a light-weight 5-switch pedal board that is great and easy to use (optional), in addition to two foot pedals.
After you get the Korg, you will think "why did I do this", but after playing it and getting used to it, you will say "I LOVE this thing!"
Ask any specific questions if you wish.