I picked up the low-end Lumix LZ8 and also a Sony W120 for my girl (it's more stylish.) I paid approx. $120 each. The Lumix has a bit more flexibility, and I like the controls/menus a bit better, and it has a great hi-speed burst mode, although at smaller (2.5 megapixel size.) Also, it uses the same SD cards I use for my D50. However, I also really like using the little Sony. It's metal, slimmer and actually focuses and responds faster, just seems a bit more snappy. The menus aren't as intuitive, but once you get used to it, it's fine. The Sony LCD display isn't as high res as the Panasonic, but it's not a big deal. The Lumix uses AA batteries, and I really recommend getting rechargable lithiums or you'll be going through batteries. The Sony (naturally) uses it's own proprietary battery, and they cost over $40, as well as it's own memory stick format. I did pick up a 2GB memory stick for $12.
In the end, I like them both. They both were the top choices in DPReview's budget p/s shootout. Both have good lenses (Leica and Zeiss) and start out around 32mm equiv. The Lumix has a longer zoom. You might want to look at the next level Lumix cameras, as they have the slim metal models, and the slightly less slim metal AA versions with longer lenses. The lower end LZ8 has a plastic body, but in black it looks fine, just not quite as flashy as the super slim metal cameras.
Both are pocketable for the most part. (just don't sit on them...)
Canons have always been the dominant maker in this category of cameras, but I think taking a serious look at the Panasonic Lumix line, and the Sony DSC-W series would be really worth it...
I haven't used the video mode much yet, but the Lumix has an option for bigger video than the Sony, if that matters.
