Longer focal lengths create less dof at the same subject distance, and with full frame u use longer focal lengths to achieve the same composition as aps. A 35mm f1.4 on aps may produce the same exposure and composition as a 50mm f1.4 on full frame, but it will have a wider dof due to the wider focal length. If u use the same lens on both the aps will have less dof due to the fact that you needed to back up 30% to fit the subject in frame.
An extreme example of this is found when you shoot large format film. This photo was taken at f2.5 on 4x5" film:
4x5 Aero Ektar Polaroid | Flickr - Photo Sharing!
2.5 isnt an extremely large aperture on small format, but it's very large for 4x5, you'd need a f0.75 lens to achieve this on a full frame dslr due to its much smaller sensor area compared to 4x5" film. You get the same effect when going from aps to full frame, just to a lesser degree.