Autofocus on some compact cameras is fantastic. For the tests I've seen between the V1 and the NEX7, the NEX beats it in every test except single point autofocus where the lens is already set to the correct distance. I expect the Nikon has better low light performance but autofocus isn't everything...far from it. I admit however that these tests can be somewhat subjective. From experience i can say that the NEX-7 is very fast and autofocus is quite capable.
Everyone forgets that the V1/J1 ONLY uses phase detection in good light. When light levels drop, they default to contrast based AF which has pathetic performance according to DPReview:
"Assuming that the light level is high enough, then the J1 and V1 switch to a 73-point focal-plane phase-detection AF system that offers fast and responsive 'single-shot' AF and impressive continuous AF tracking performance.
The switch to phase-detection AF depends on the amount of light falling onto the cameras' sensors, which is dependant on lens aperture as well as ambient light levels...
The J1 and V1's contrast-detection AF systems, which take over when light levels are too low for effective phase-detection AF (and remember that this is the camera's decision, not the photographer's) are less impressive. Focussing is less positive (AF wobbles quickly around the target rather than locking straight on it) but impressively accurate when it gets a 'lock'. The problem is that even in average interior room light, both cameras struggle to find that lock.
They rarely give up completely (and built-in AF illuminators are on hand in both cameras) but we've been surprised by how frequently they falter."
- from http://www.dpreview.com/reviews/nikonv1j1/8
And that is the complete picture of V1/J1 AF performance.