The P6000 holds up well against the Panasonic LX-3, with both of them being similarly sized. The G10 is quite a bit heavier and bulkier, with the trade-off being its higher image quality, better build, and superior features over the P6000, such as a multi-frame raw buffer and live histogram.
What unbalances the equation is that at this time these two cameras are priced the same. If the Nikon were lower priced I could see an argument for it, but not at $500. The LX3 offers an even smaller size, variable aspect ratios, and a usable raw buffer, along with a lower price. Add to this a wider and faster lens, if that's what your style of shooting needs, and regrettably the Nikon P6000 then finds itself uncompetitive with either of the other two.