The theory makes sense, performing a bench press or military press on a Swiss ball should engage more of the stabilising muscles of your core. In reality, though this isn’t the case. A study released by the Human Performance Laboratory at California State University, suggests that abdominal muscle activation during a three-rep max chest press and shoulder press was similar whether performed on a Swiss ball or on a flat bench. Performing these lifts on a Swiss ball does have some benefit, however. It’s just not in developing core strength. Those lifts work the stabilising muscles of the shoulder, not the core. If you were to use the Swiss ball for that purpose it would have to be somewhere in the range of 15 to 25 repetitions with low weights.
Basic lifts on a stable surface, provide a better overall stimulus. A heavy squat, deadlift or military press is always going to be more effective at activating the core than any Swiss ball lift.