Ball chairs have become very popular, Amazon sells the BalanceBall and probably the best way to answer your question is to read the Amazon reviews of it. A lot of them are quite detailed and will give you a great insight into the product.
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I have had that exact chair at work for over a year now. It is very comfortable and I guess more engaging for the core muscles…hard to notice something like that, it’s so subtle.
Pros:
It is easy to take 5 or 10 minutes during your day and stretch or work your abs.
Cons:
It doesn’t swivel or go up or down. Although you can adjust height a bit by inflating or deflating the ball.

Overall, if it will be the right height for your desk I would recommend it.

I have tried them, they are very comfortable. And of course, you can use the stability ball independant from the chair for workouts.