Agree with your first statement, but not completely with the second. If you stay at the same distance, but use a different focal length to get the same image, the smaller sensor will have deeper dof and less blur. That's common field experience I think.
I don't believe I mentioned using a different focal length to get the same image. Using the same focal length, same distance, the crop sensor will have shallower DoF (and obviously a tighter framing). Try it yourself - go to DoFMaster
, pick a focal length, aperture, and distance, leave them constant, and set the camera to a 5DII vs. a 7D and see what that does to the DoF. For example, 5DII, 50mm, f/1.4, 10 ft = 1.02 ft DoF whereas 7D, 50mm, f/1.4, 10 ft = 0.65 ft DoF, i.e. shallower with the crop body.
I mentioned compensating for the effect of sensor size on angle of view by changing distance to subject, but of course you could also compensate by using a different focal length. You're right that if you change lenses (or zoom) to keep the angle of view the same when you switch sensor formats, the crop body will have deeper DoF (e.g. for the example above, keeping things the same for the 7D, but comparing a 5DII, 80mm
, f/1.4, 10 ft = 0.39 ft DoF, shallower with full frame).
So, the point is that if you keep the framing the same (however you do that - changing lenses, zooming, or walking), the FF body will have shallower DoF, but if you keep focal length, distance, and aperture constant, the crop body will have shallower DoF.