I'd go for the G3 personally, I don't like the fact that although on the Sony you get the advantage of larger sensors, the lenses that you need to mount onto the body are huge, defeating the fact. If I were to choose another brand, I'd probably go for the Olympus E P3, mainly because of its selection of quality lenses (including many excellent primes), good image quality, fast AF and beautiful styling.
If you want something nice and small, you may want to consider the Pentax Q or Nikon J1 or V1, either one with a small pancake prime lens. The Pentax and Nikon both have smaller sensors (although their image quality is still very comparable), allowing them to be smaller than the other cameras. They may be a bit out of your budget, but you won't be disappointed with either one.
Regarding the "Leica" logo on the Panasonics, it's mainly marketing. I believe that the lenses do use Leica optics, but they're nowhere near the quality of those that you'd find on one of their M series rangefinder bodies. The quality of the Leica Lumix lenses for the Panasonics is very similar to those of other brands, they're not superior or inferior to them.
Gear: 7 Nikon Nikkor AI-S and AF-S lenses, SB-700 flash, Nikon D7000, Nikon FM, variety of accessories
"There are no rules for good photographs, there are only good photographs."
- Ansel Adams