Hi:

I had use the Ketron SD1s for almost 5 years, is a wonderful instrument, if you need a lot of different patterns for a Jazz oriented performance, you may fall a little short from the factory styles, you may have to add either converted styles from other boards etc. Is easy to "mute" the unwanted parts, no need to go to menus, with the left side buttons, but for a more consistence use and faster way to recall them would be using the registrations. The XD9 is smaller than the SD1+ and it would have the limitation of how many styles/patterns you can have, even with the 2 meg memory expansion that is a most, I would probably wait for the release of the SD5 in that case, but I probably scratch this model out (XDs).
The Korg depends on what model you want to use, and I also would use their "performance"=registrations too. In the PA1Xs you have the sliders that allow you to control the volumes in a similar way the SD1 does. In the PA80/60/50 you most enter in a menu, Mixer, then part then muted them, I would save the changes.
Probably the easiest of all, it would be the Yamaha Tyros2, easy to mute parts and I also would save the changes in registrations, one more thing, there are LOTS of styles for this brand, even more than the others.
I had use the Ketrons, Korgs and Yamahas for many years and I do perform mostly standards and ballroom music, if you have more questions, send me an e-mail. I did have for around 4 months the Roland VA7 when it came out and got rid of that, I would not recommend you that, and as far goes the GEMs, I did audition them, and I found them a "tad" short in quality vs the Ketron, I put it this way, Gem=Yugo and Ketron=Mercedes. Of course this is MY perception on their sounds, styles, user interface and SUPPORT.