Currently, the Lumix SZ3 is the lowest priced Panasonic Point-and-Shoot digital camera that comes with a Leica-licensed lens. And the DSC-W730 is the lowest priced Sony that comes with a Carl Zeiss-licensed lens. Leica and Carl Zeiss are legendary German photographic lens designers who are known for their super sharp and accurate color lenses. Not all Sony and Panasonic cameras have Carl Zeiss and Leica marking on the lens, respectively. Those that do not cost less, but I always choose ones that do.
I have both of the above cameras and like them very much because they take excellent, sharp, color accurate pictures without costing a lot of money. The Panasonic costs a bit more, but both are excellent.
The Lumix SZ3 has a slightly greater zoom range of 10X, compared to Sony's 8X. Both cameras have the wide end of the zoom lens at 25mm (35mm film camera lens equivalent), which is great for group and scenery shots.
I prefer the SZ3 camera's physical user interface, especially the direct "movie button" and the shutter button surrounded zoom lever. They are more convenient and easier to use than Sony's.
The SZ3 shoots video in 720p at 24 frames per second (fps). Some users like this frame rate because the resulting video looks more film-like, or movie-like than when shot at 30 fps or higher.
I buy extra compatible batteries on eBay. For the SZ3, you can typically get 2 new batteries, with free shipping, for about $13. Just search "Panasonic SZ3 battery".
The black version of the SZ3 also comes equipped with a black-colored lens barrel - a rarity these days. IMHO, it makes the whole camera look better/more consistent.
If you need a carrying pouch for this camera, I'd recommend Case Logic's DCB-302 (less than $6) Case Logic DCB-302 Compact Case for Camera - Black. Its size is just right for the SZ3, with a few centimeters of extra space so it isn't too snug. The small accessories pocket is perfect for memory cards and batteries.
Instead of using the pouch's shoulder strap, I urge you to tie the camera's wrist strap to one of the two shoulder strap ringlets, so that the camera and the case are loosely tied together. The arrangement permits me to hold the case with my left hand while I take pictures with my right hand. If someone bumps into me at this moment, my camera is less likely to fall to the ground, as its wrist strap is tied to the case held by my left hand.