Yeah, i should have terms that better. If you want shallower. You'd get the true DOF from a lens on full frame compared on cropped. Even on a 1.3 cropped camera, you'll get a little shallower than 1.6.
You always get the true DOF from any lens. The size of the sensor does not change the laws of physics.
If you choose a lens that will frame the image the same from the same position, such as a 50 mm lens on an EF-S camera and an 80 mm lens on a FF camera, take identical pictures and enlarge both to the same size print, you will get more depth of field on the print taken with the EF-S camera.
Whether this is better or not depends on what you are trying to do. If you want to blur out the background, the shallower depth of field of FF will be better. If you want to keep foreground and middle ground elements in sharp focus EF-S will be better.
It is slightly more complex than that. With an EF-S camera the image has to be enlarged more to get the same size print and you are using a shorter focal length. This means that the effects of diffusion/diffraction from a small aperture are more pronounced so while you may not want to shoot at a smaller aperture than f/11 on a 50 mm lens on EF-S, you may be able to shoot at f/16 with the 80 mm lens on FF. This almost negates the greater DOF advantage of EF-S. Similarly, if you want to blur the background, most people will consider how they set up the shot (more subject to background distance and less cluttered background) and what lens they choose (more telephoto) before deciding to change formats.
