Well you already know my experience and decision. First, it's not fair to compare S970 to top of the line Korg, except to say they are the same size and nearly same weight! You can use the same bag to carry them in.
As far as Tyros: too bulky, no touch screen, mediocre drums (except audio), too expensive, no multi-switch foot controller except the too-big, too-expensive MFC10.
I also much prefer the joystick to wheels, but that's personal. So many more real-time operating controls, including multiple programmable sliders and buttons. Excellent vocal processor and harmonizer. Universal power supply, dual midi/MP3/CDG players. Korg finally has guitar sounds as good as Yamaha (about time). There is also a fantastic new piano in it. I much prefer Songbook to Musicfinder.
Yamaha still gets points for easy access to external styles, availability of 14 million styles, although 13.9 million of them are duplicates or edits.
Yamaha has the PSR Tutorial forum going for it, although Yamaha has nothing to do with it. Thanks Joe!
Yamaha has polished, CD-like sound. Korg has more live, exciting sound. Yes, both can be edited, but not totally. As far as editing, Korg lets you do things on the fly easier. For example you can change and save most things while the style is running.
Korg periodically issues updates that include new styles, free of charge!
I could go on. The good news is that there is not a bad choice. Play whatever you like best and that you feel suits your needs and taste. They are both wonderful!