With 4 NiMH AA batteries installed the weight difference between the two is negligible. But the IS 1 is physically more compact.
Iím not as big a fan of NiMH as some. I have a camera that uses them and it can be a hassle. NiMH batteries lose a lot of charge just sitting where the lithium batteries donít. Unless the camera has a design fault you can leave a fully charged lithium battery in the camera for weeks, pick it up and start taking pictures. Or insert your spare battery without having to recharge it. You have to recharge the NiMH batteries regularly. I got a spare for my FZ10 from Eagle for $20 and it has been excellent so far.
The FZ10 has a pitiful built-in flash. And they add to the hassle factor by making you remove the lens shade before you can use it. You get much better flash shots with an external flash unit, and you can pick up a small non-dedicated automatic unit with a bounce head inexpensively. You would get nicer flash shots with either camera with an external flash. But if you just want to grab a flash shot and have only the camera with you the FZ10 is limited in the flash range.
I donít find the FZ10 hard to hold well. You cup your left hand under the lens with your left elbow in your chest with the right hand and elbow in the normal good shooting position. There is a valid complaint that the location of the EVF prevents you from using your forehead to help with stabilization. The rubber eyecup I put on mine seems to provide that missing stabilization. You probably want an eyecup with the FZ10 in any case.
Image stabilization is a great feature. Not only for long telephoto shots in less than ideal light, but for wider shots indoors without a flash. You need pretty good indoor lighting to shoot without a flash or tripod even with stabilization, but the situations in which you can handhold are much greater with IS.
I havenít seen any reviews of the S1. I would wait for some good reviews and handle one in a store before making a decision. 4Mp is skimpy for my use and 3Mp would be unacceptable, but that doesnít apply to everyone. If you are sure you wonít ever want a blowup larger than about 8 X 10 the S1 might be a better choice. I agree the greatest camera in the world isnít going to do you much good if it is sitting at home.
Checksix Ask on the Panasonic forum. Several people handled them in stores Ė they might be able to direct you to a chain that carries them.