I had the original ZS-3 which served me well until it broke down. I purchased the ZS-10 and was disappointed with the low-light performance to the extent of returning it. The ZS-20 is a major improvement over the ZS-10.
I have taken only 100-200 pictures but the low light performance is much better and comparable (or slightly better) to the ZS-3. I don't have hands on experience with the other supercompacts but the panasonic worked well for my needs

Pro's
-The Zoom is phenomenal (but comparable to other super compact out there)
- AF speed is very good.
- Low light performance is ok (major improvement but still just ok)
- Flash works surprisingly well to improve overall picture quality
- Small, easy to carry around
- Same battery as previous model, so if upgrading, you can re-use old peripherals

Con's
- Menus could be better, 2-3 clicks to get somewhere, too many buttons and dials *** see update below
- Touch screen is... Read more

Just got this camera, and have owned its three previous models. One thing for all to note if you are familiar with this series is that the battery must now be charged in camera with a short USB cable to a Panasonic wall charger. For me, this is a disadvantage, since I have enjoyed the flexibility of the previous arrangement -- a dedicated charger into which the battery is placed outside of the camera. I found this "old" setup to be more convenient and easier to use when traveling, and easier to pack. Maybe this is not a problem for you, but it was an unpleasant surprise for me. As others have noted, though, the old charger works with this battery (same battery as before), so you can easily purchase a stand-alone charger.

Update 4-6-12

I have now taken some representative shots with the camera and have some observations. Like the previous three models, the display on this one is not ideal in bright sunlight, although it is acceptable. To my eye, the photos are... Read more

I had the Panasonic zs7 which was a 12x Zoom. I took pictures with both cameras side by side and the quality of the picture id much better and the extra zoom is great. I like how they have a button right on top for Manual control and you do no have to go though the menu as much as the other model.Once you play with all the feature and read through the book it is pretty easy to use. It has GPS but I do not use it and I have not gone through the 3D mode. It is the smallest camera I've seen with 20x zoom. Width is smaller than my Smart phone and its about an inch thick. Full charged I used the camera for the whole day. I like how the charger is USB or wall.