The IS of the canon counters camera shake that with tele photo shots and with lower light conditions (longer exposure times) prevents blurry pictures from camera motion. With longer exposure times a moving subject will still be blurry though.
The Fuji with its higher ISO with low noise possibilities allows for shorter exposure times, and will not show up camera motion because the time is too short for camera shake to show up. With the same ISO value as the Canon it will not give assistence with tele photos, and with its shorter exposure times with high ISO in lower light conditions moving subjects will be less blurry than with longer exposure and IS.
Both systems have their pro's. Both cameras are very capable and nice. It depends on what one finds important and what your preferences are, what camera is best for you. I do like the S2IS's screen a lot, that is a feature i would find important when I would choose between the S2 IS, the S5200/5600, the FZ20. Others will have an other prefference.
And MaryG, I am VERY glad you are happy with your new camera
I do not remember if I have pointed ou to the S5200 or not, but anyway I am very glad you found a camera that you like a lot. And yes, your dog is very adorable