If you're going to compare which camera will give you shallower DoF, you have to do it for a given FoV. It makes no sense to compare different pictures (say, a portrait and a medium shot).
If you had to take a portrait, and could use different cameras, what would DoF be like on each of them? Well, it depends on sensor size and f-stop. Period.
The following options will give you exactly the same picture, in terms of FoV, DoF, exposure
* 50mm lens set at f/5.6, 1/50s and ISO 1600 on a full frame camera
* 31mm lens set at f/3.5, 1/50s and ISO 600 on an APS-C camera
In all three cases, field of view, depth of field and exposure will be absolutely identical. And also compression, face distortion because of perspective, size of out-of-focus highlights... The images will be basically identical, except for whatever differences in sharpness and detail the different sensors and lenses introduce.