In which I question the NEX APS-C Shallower DOF argument

Depth of field varies with a many factors, but at the time of shooting the key three factors are distance, field of view, and aperture size (not f number but actual aperture diameter).  Because larger sensors always allow longer lenses to give the same field of view, they achieve narrower depth of field (thanks to the larger apertures on the longer lenses).

With a Nikon 1 kit lens 10-30 lens the aperture varies between a maximum size of 3.5mm (10mm/3.5) and 5.3mm (30mm/5.6).  Using the NEX kit lens, the aperture diameter varies between 5.1mm and 9.8mm.  A 35mm sized sensor with a similar kit 28-70 f/3.5-5.6 would have maximum apertures of 8.0mm to 12.5mm.  All three would be able to have the same field of view at the same distances so the aperture becomes the main factor in the depth of field (presuming they were all viewed with the same final image size).

Viewing the images at the original size makes it clear that for similar framing, distance and aperture settings the depth of field varied quite a bit between the three:

http://www.stevehuffphoto.com/wp-content/uploads/2011/11/m9andnoktonf4.jpg

http://www.stevehuffphoto.com/wp-content/uploads/2011/12/nex7andnoktonf4.jpg

http://www.stevehuffphoto.com/wp-content/uploads/2011/12/nikonv1f4.jpg

Imagine a portrait taken at 135 f/2.8 of a person's head and part of their shoulders on a full frame camera.  If we want to use a 4/3rds body to do something similar there are three choices, back up 2x as far with the same lens (increasing the depth of field by roughly 2x and changing perspective), switching to a 75mm lens (we would need an f/1.4 lens to match the aperture diameter of 48mm) or if the same lens were used at the same distance, the result would be a much smaller framing (it would likely be a very tight framing around only the face).  The one way smaller sensors can "fake" the look of the bigger sensor is via a composite of many images taken with the longer, faster lens.  There is some interest in using this technique to mirror the narrow depth of field allowable on medium format wide angle shots.