The Nikon 1 can use F-mount Nikkors via a Nikon adapter, with AF-S function, and shares batteries with the D7000. These factors, alone, prompt me to favor the Nikon 1, in spite of the smaller sensor. (My wife shoots with a D7000.) Lenses are expensive!
NEX cameras do have APS-C sensors, with all of the advantages of the relatively larger sensor. While Nikkor glass can be used via aftermarket adapters on a NEX, there is not only no AF, but (unless I am mistaken) no means of electronic focus confirmation with MF, which my aging eyes really do need.
The Nikon 1 V1 has a viewfinder. This is an advantage for the V1, for my preference, though accessory viewfinders exist for NEX, and the future NEX-7 will have an integral viewfinder, so this is not an absolute factor.
I have seen a video tutorial of the V1's menu system, which makes me favor it over the menu of the NEX that I handled at a Sony Style store.
These are just my thoughts, having considered both of these cameras, but owning neither at this point. I should add that I use DSLRs at work, and for serious shooting on my own time, so either of these little cameras would play a very minor for me. This lessens my need for an APS-C sensor in a pocketable camera.
I would like to see the V1 sold with just the 10mm pancake as its kit lens!
Canon 7D2/7D/5D/40D/1D2N/M3; Nikon F6/D700/FM3A/1Dx/Coolpix A; Canon 40mm 2.8 STM, 135L, 50L, 35L, 50mm 1.8 I, 100mm 2.8L Macro, 10-22mm EF-S, 400mm 5.6L, 16-35mm 2.8L II; Nikkor 50mm 1.2 AI-S, 50mm 1.4G, 50mm 1.8D, 16mm 2.8D Fisheye, 180mm 2.8D, 100-300mm 5.6 AI-S, 45mm 2.8 AI-P, 14-24mm 2.8G, 24-70mm 2.8G, Micro-Nikkor 60/2.8G; Voigtlander 90mm f/3.5 SL II, Zeiss ZF.2 2/135 APO