Given the choice between these two, you should get the Panasonic. They use a better quality of lenses (and apparently bigger lenses in this case, which is also good), the shape of the grip area on the right side will make it easier to grip securely for stability (which the slightly greater weight should also help with), the controls have a better layout, and the range of shutter speeds is wider. It also has a trick feature the Kodak doesn't: audio recording with still images (which helps save data space compared to video if you don't really need video). The Kodak does have a couple of features the Panasonic doesn't have, but one was such a minor gimmick I already forgot what it was, and the other is Kodak's "EasyShare" system, which I don't see any reason to deal with. (It only does things you can already do anyway, but cuts corners along the way; for example, you can connect the camera straight to a Kodak EasyShare printer, but you can still print with other cameras without that, and cutting your computer out of the loop takes away your editing options and control over print job details like cropping.) I'm not too happy with the range of aperture settings on the Panasonic, but Kodak's spec page doesn't even give its aperture range at all, which there's probably a reason for. It's probably similar to the ranges on a lot of other compact cameras.

If I were you and had already narrowed it down to these two, I'd actually change the Panasonic option from TZ5 to TZ4 and still get that rather than the Kodak. The TZ4 is the same camera as TZ5 in all ways but one: slightly fewer pixels. But on these compact cameras, higher pixel counts are a bad thing. The way they get them is by making the pixels tinier and tinier to cram more and more of them onto the same sensor size. But a tinier pixel can't collect as much light, so they have to compensate by being ultra-sensitive, which makes them more prone to "noise", which looks like film grain. The result is a bigger but grainier picture. The only way for high pixel count to be an actual improvement would be if the pixel size didn't shrink but the sensor size grew... but then you'd need the lens to be farther away from it and bigger, and then it wouldn't be a compact camera anymore. 8 MP is already plenty for printing 8" pictures, and you won't get up to poster size without going well over the 9 MP you'd be getting with the TZ5 anyway, so the extra megapixel in the TZ5 (or the Kodak you've picked) wouldn't gain you anything except more graininess in the picture and a higher price.