I'll start off by saying I've a very happy S3 owner, so I'll try to keep my bias down to a minimum.
A couple of places I can see where the S3 has an advantage: the S3 has a better Macro mode (SuperMacro focus distance goes to 0cm!). The S3 has Manual Focus and White Balance controls, too. The S3's got a better continuous mode it's 2.6fps, the Kodak can only sustain 2fps for 6 frames. Flip-out, rotating LCD.
Where the Kodak has the advantage: it's got more internal memory (32M) the S3 has none and won't take any pictures without an SD card. It's got higher ISO settings (but this isn't necessarily a good thing as really high ISO on these P&S cameras are often awful). .5" Bigger LCD. 1 more MP.
To me, better manual controls, macro, high-speed continuous and the flip-out LCD are worth more than internal memory, higher ISO, and a bigger LCD.
However, you're already familiar with Kodak software and have it on your PC.
I don't think you'd be disappointed with either camera, really....