I have the S3, and I've just checked out the S5 in one of the local stores... it seems they've improved the design and increased the resolution.
From my own perspective, the S3 is a fantastic camera... had it for almost one year, but I'm still amazed at the thins it can do, and I love the fact that it records video that is indistinguishable from regular DV footage.
Looking at the Kodak, I must say I'm impressed with the specs - the video is even better than the one on the S5. Two weaknesses I was able to spot quickly while looking at the specs are the complicated battery arrangements (can't beat the price and availability of regular AAs) and the lack of a swivel screen - which is an extremely useful feature, as a matter of fact.
Do what I did - go to a photo store with your own memory card and have them let you examine both cameras in depth, and take a few snapshots on each of them, using your memory cards... then go home and look at the images, play with them in Photoshop and see which ones you find more pleasing. Features aside, that's what counts in the end.
Good luck!