There will be a difference in the depth of field, if
you frame the shots identically the FF sensor will give a shallower DoF, by a factor of 1.6 when comparing FF to APS-C. So, the APS-C will give a depth of field equivalent to setting the aperture on the FF camera 1.3 stops narrower (because stops are a base-2 log scale, and the base-2 log of 1.6 = 1.3). Put another way, 85mm f/1.2 on a crop body is approximately equivalent to 135mm f/2 on FF, 135mm f/2 on APS-C is approximately equivalent to 200mm f/2.8, etc. Again, this applies if you frame the shots the same on the two bodies with the same lens.
The reason is distance - because 85mm on APS-C yields a field of view equivalent to 135mm on FF, to get the same framing you must be further away with the APS-C camera. That increased distance results in a deeper DoF.
You can prove it to yourself with the numbers, plug whatever you like into DoFMaster's DoF calculator
. They also have a page on the effect of crop on DoF
As a side note, this isn't bokeh. Technically, bokeh is the quality
of the OOF blur, and is a property of the lens and the elements in the picture. A crop sensor affects the quantity
of OOF blur.
Well, ok, that's a simplification, since a crop sensor can affect bokeh with some lenses - in some cases, vignetting results in OOF blur spots at the edge of the frame that have a cat's eye shape, which is less pleasing than a round shape, and to the extent that using an EF lens on a crop body reduces vignetting, it will result in rounder OOF blur spots, which would be considered better bokeh.
Hope that helps...