I've used both of these cameras a little bit (it's my job!). They're both excellent cameras, both have their pros and cons, but the S2 has the edge.
The S2 records video in stereo sound (unheard of!) and at a very high VGA resolution. Canon's autofocus-assist lamp is unbelieveable and very handy and reliable. The custom white balance works great, as does the image stabilizer (which means very reliable color balance and fewer blurry pictures). The lens in this camera is unbelieveable too -- its ultrasonic motor is the best on the market. The LCD screen is small, but the flip feature is pretty cool. It takes 4-AA batteries, which sucks, but the battery life is better than other 4-AA point and shoots. I'd rather have a lithium-ion rechargeable, like the P850 uses.
I've also heard that Canon uses a better CCD sensor than Kodak's and it is supposed to be able to produce more accurate colors, but I haven't noticed much of a difference in the prints. The Kodak has a hot shoe for an optional external flash, located directely above the lens, which is great. Canon offers a slave flash for the S2, but the camera sits in a crade and the flash is off to the side (creates weird shadows and effects).
You can get optional lenses and filters for both cameras for about the same price, but the Canon requires a special adapter for them, which means more money.
Anyway, I'd still go with the S2 because it does have more useful manual functions and the video mode is unbelieveable -- almost as good as a quality digital camcorder. But, on the other hand, the Kodak is easier to use and learn and does have better battery life.
Good luck deciding!