A given lens/f stop/focus distance combo has a given depth of field, period, end of story. The sensor has nothing to do with it.
Here's an intuitive way to look at it. Put a (say) 100mm lens on a full frame SLR and set it to f/8. Focus at 20 feet and take a pic. The image has a certain DOF. Now magically replace the full frame sensor with a 4/3 sensor, changing nothing else. Take a pic. Do you think the DOF would change? Of course not - same image projected on a smaller sensor. Same experiment could be done by taking the full frame image and cropping it in PS to 4/3 size. So, the sensor has no DIRECT effect on DOF.
There is, however, an INDIRECT effect. The 4/3 image takes in only about 1/2 the scene of the full frame image. This is why they say "200mm equivalent," but the fact is it is still a 100mm lens. So, to get the same scene with the 4/3 sensor you would have to back away from the subject to about 2x the distance. And, you would have to focus the lens at 40 ft, not 20 ft. And, focusing further from the camera results in greater DOF for any lens. So, smaller sensors give greater DOF INDIRECTLY by forcing the photographer to be further from the subject.