We've had this before. If you view both images at the same size then the APS-C version will show a smaller DOF because it is effectively a blow-up of the wider image captured by the FF sensor. Xarqi's circles of confusion are therefore magnified more, making visible the ones that were only just small enough not to be visible in the FF image, and therefore look unsharp, in the APS-C version.
Of course, the two images would not look the same because you kept focal length equal, resulting in a different field of view for each sensor size.
EDIT: Dammit, you said "same camera". MY comments all refer to the use of different cameras to match the image circles of the two lenses. With the same camera, as xarqi says, you haven't changed anything. Apologies for any confusion, circular or otherwise.
Mark.