My thoughts are that the big ball strengthens the lower back. I find it very comfortable, much more than a conventional chair. I started to use it for a few hours a day to improve my core strength for horse back riding. Then I noticed that my posture was getting better--kinda like a positive side effect
And I think that it is good for abdominal muscles. I have also read on the internet that you burn more calories throughout the day if you sit on one as opposed to a chair.
I started for a few hours but would switch back to my normal chair for lunch. Now I just use it all the time. But when I'm feeling lazy I often don't want to use it but I force myself to.
I think that the best way to use it is to sit with your legs on either side of the ball rather than in front for easier balance.