Stability - a load of Balls???
I'm not a big fan of Swiss/BOSU balls. Although I do feel these can offer a 'challenge' in testing one's balance ability.
There is no doubt they are a common sight in gyms, and the argument often used to justify their proliferation is an increase in core engagement because of the additional inherent stabilisation required by the body.
A recent study by Brandon Uribe and his team casts doubts on their effectiveness. The investigation tested muscle activation performing presses (bench/shoulder) on a fixed bench versus a stability ball. They tested the muscles involved in this activity (including the abs) and they concluded using an unstable surface made no difference during muscle recruitment.
Makes you wonder why you would bother using a nonstable surface - if there is no gain? I can think of a good reason to be as 'stable' as possible though (apart from safety). Using a stable support is more likely to increase total muscle activation due to the greater loads possible during lifting i.e. you can go heavier with a solid platform!
To test balance simply perform an exercise or activity you normally perform bilaterally (i.e. on two legs) and do the same on one leg - such as a squat. Or even perform an exercise with your eyes closed such as a deadlift. You will most likely find the above a significant challenge to the stabiliser muscles, without the use of a 'ball' of any kind.