DOF is the same for both formats, the difference is in the field of view.
If you shoot a subject with both formats using a 200mm lens at F2.8 and fifteen feet away, the DOF is the same. The difference is you would be seeing less if the subject with the "crop" format due to the increased magnification. So, to get the same framing as the the "full frame" camera, you would have to move back with the crop camera, which would put the subject at a greater distance away, and also changing the relationship of the subject to the background, resulting in more of the background being in focus.
This is true regardless of focal length...the crop camera will always have to be farther away from the subject to keep framing the same as compared to a full frame camera (with the same focal length lens). Of course, you can change focal lengths to a lens with a similar field of view (a wider lens), but that lens will have different DOF characteristics. It's all about the relationship of the subjects distance from the camera, the background, and the F-stop used. Of course, in theory, with the right focal length and F-stop you can create a similar shot to a full frame camera at the same subject distance, the problem is that in reality, there may not actually be a lens option to do so (more of a problem with on the wider end of things).