If your objective is to have more background blur, then FF is your friend. FF has shallower inherent DOF, plus there are more wide aperture EF lenses available than EF-S lenses.
Which makes it sound like FF (i.e. the larger sensor) somehow impacts DOF all by itself.
There is a useful rule of thumb that is worth noting, but which boggles the minds of many. The rule is that for equivalent framing, the DOF depends only on format (MF or FF or crop, etc) and aperture. Check it out. (Don't forget, though - equivalent framing!!)
Now there ya go! That "equivalent framing" part says that you can't just change sensor size without changing the lens. So my quick test was to figure out which of those 2 changes actually affects DOF.
The other thing useful to note is that longer lenses, even though they give the same DOF as wider lenses (with equivalent framing), give a more pleasing bokeh because of the perspective change.
I think I disagree here on a somewhat minor but important part. Longer lenses give shallower DOF than wide lenses "at the same perspective" regardless of the sensor size. Stand in one place, shoot the same scene with 2 cameras, 1 lens and you get the same DOF. It isn't the sensor, it is the lens and the perspective.
Once you crop the FF image to use a sensor that is exactly the same size as the 1.6X format you are comparing it to, the camera isn't (functionally) a FF camera any more. Put another way....a FF camera doesn't make a shallower DOF image just because there is a FF sensor in there someplace.
Thanks JeffreyG, this is my point.
You just compared a 1.6X format camera to a 1.6X format camera and discovered that they make the same image. Don't slap yourself in the forehead too hard with this eureka moment.
Cropped FF vs APS-C was the purpose of the test. I was wanting to confirm what happens to DOF in the focal-length limited scenario which is where I often find myself while shooting sports.
And the eureka moment was mostly a tongue in cheek statement. I forgot the smily face in the thread title!