Both are quite compact mirrorless cameras without a grip, without a flash shoe, and with fixed LCD screens. You can't put an eye level viewfinder on any of them. Both are mounted with rather similar wide angle pancake lenses in the picture above.
Also, since the Nikon 1 J1 is the very first generation mirrorless camera from Nikon, and the cheapest, it may look strange to pitch it against the Lumix GM1, which is a new, premium camera from Panasonic, widely seen as the leaders in large sensor video.
However, the Nikon 1 family of mirrorless cameras has something which Panasonic has never implemented: On sensor PDAF sensors. Panasonic have decided to rely on CDAF, which requires more image processing power to function well, but has the advantage of not sacrificing any pixels for PDAF sensors. In theory, PDAF should be able to give a much better AF-C performance, and AF performance during video recording.
You may also think that the Lumix GM1 is not a very good video camera, as it appears to be styled in a classic way. However, in my experience, it performs just as well as, or even better than, the GH3 in terms of image quality, quality of ETC video, and AF during video. So the GM1 is pretty much state of the art, except for the fact that it doesn't have 50/60 FPS 1080p video, and of course, it doesn't have 4K video.
To see how the Nikon 1 J1 camera performs in terms of autofocus, I mounted both to a Desmond Mini Dual Camera Bracket, typically used for stereo photography. The lenses are the Lumix 14mm f/2.5 and the Nikon 1 10mm f/2.8. I set both lenses to f/2.8.
For the test videos, I set the ISO to 200, except when otherwise noted. Here are the results:
As you see, the Nikon 1 J1, despite being two years older and cheaper, is way better in terms of acquiring focus. Even when panning quickly, it gets the focus right almost instantaneously, and even in poor light and high ISO.
I would say that Nikon is the only company which got PDAF for mirrorless cameras right from the beginning. The AF performance is just amazing.
Now, these videos are not typical of how people normally use video, but they illustrate the strength of the Nikon 1 system. Also, the 27mm equivalent wide angle pancake is not the one which needs fast AF the most.
However, with the recently launched Nikon 1 70-300mm f/4.5-5.6 lens, the Nikon 1 system will be the first to be useful for birders.
At no time before has there been a so small and light interchangeable lens system with this reach: More than 800mm eqvivalent. And with the fantastic AF performance of the system, this lens should be useful for catching birds in flight (BIF). Especially with a camera like the Nikon 1 V3, which has a proper grip and EVF.