Hi Yitzchok
NOTE: These are my personal observations; however as always try before you buy. (Never under any circumstances make a decision using just online demos)

The typical life cycle of a Yamaha is 3 years, so it’s good for some time yet.

The Yamaha is a pre-set instrument that is aimed straight at the home player, therefore everything is done for you, (Balance, Style levels, voices etc.) so is good to go straight OOTB.
The Korg, although designed for the home player, is a trickle down from their Pro-Line so maybe not quite as well balanced OOTB, but its flexibility makes the Tyros 3 look like a Karaoke machine.
If you’re used to the way Yamaha do things, then there is quite a learning curve when moving over to the Korg OS.

SOUNDS:
Compared to the Tyros 2, I find the Tyros 3 to have a very compressed Mp3 type sound, whereas the Tyros 2 was CD like. (Exceptions are the SA2 voices)
The Korg on the other hand sounds more like a live performance, (Which is always my preference) but is not for everybody.

SA2 sounds are superb, (Although VSTi have had better for donkey’s years) but limited in what you can do with them, however the Korg DNC takes articulation to a whole new level (For a hardware board) allowing you full control over the multiple articulations, however the downside is that to get the best out of them you have to put some work in.

STYLES:
The Yamaha gives you everything (Including the kitchen sink) so tend to be very song specific, whereas the Korg allows you more flexibility to play what you want to play, rather then what the style dictates you to play. (This is the main reason why Yamaha styles (Particularly IMO the repetitive Megavoice styles) are my least favourite out there)

FINALLY:
To reiterate, always try before you buy, (As it’s a very personal choice, and not one suits all) if there are no dealers in your area, go onto the respective forums (Or ring the nearest dealer) to see if anyone has one in your area that you can try. (Most will be happy to show them off)
Remember: The choice is yours and yours alone.

Hope this helps

Bill

BTW: If I was restricted to a hardware board, my personal preference would be the Korg. (Fortunately there are plenty of software boards out there, so I don’t have to make that decision)