For a given field of view for the image, and a given f-stop, a camera with a larger sensor will have more out-of-focus blur. Of course, the camera with the larger sensor will need to use a lens with a longer focal length to get the same field of view. In turn, that means that the absolute aperture (not the ratio that gives the f-stop) will have to be bigger. The absolute aperture (roughly, the diameter of the front of the lens, though things get funny for wide-angle lenses) is what really determines how burred the out-of-focus parts of the image are.
To see this, imagine that you're focused to a distance of 9 meters. That means that all the light from any point in the plane that is 9 meters away gets focused on one spot on the sensor, with this spot on the sensor corresponding to the location on the plane. Now imagine what happens with the light from a point 10 meters away. On the way to the sensor, all the light rays from this point will have to pass through the plane that is 9 meters away, and will then behave just as if they originated from that 9-meter-away plane. Since that plane is in focus, these rays will show up on the sensor in positions corresponding to where they were in the 9-meter-away plane.
Now imagine where those rays from 10 meters away that end up on the sensor actually are when they reach the 9-meter-away plane. Suppose the absolute aperture (diameter of lens) is 20mm. The rays that hit the lens (and then the sensor) starting from 10 meters away form a cone, which spreads out to 20mm at the camera. So at 9 meters away, 1/10 that distance, the cone will have spread out 1/10 as much, which is 2mm. So single points at a distance of 10 meters look just like disks 2mm wide at 9 meters. That's the extent of out-of-focus blur.
How blurry that seems to the viewer of the final image depends on the field of view, which for a fixed focal length depends on the sensor size. With a small sensor, the field of view at 9 meters might be only 200mm, and 2mm looks fairly blurred. With a large sensor, the field of view at 9 meters might be 2000mm, and a 2mm disk might look almost like a point to the viewer.
EDIT: I realize now that the concluding paragraph may be confusing, since it seems to say that it's the small sensor that will have more blur. The problem is that I shouldn't have compared images with different fields of view - when deciding which camera to use to take a picture you have in mind, you of course envision using lenses for each camera that will give the same field of view, as appropriate for the result you are trying to achieve. Looked at that way, one can see that with the field of view fixed, an absolute aperature of 20mm will correspond to a smaller f-stop for a camera with a small sensor size than for a camera with a larger sensor. For instance, a 100mm focal length lens with a 20mm aperature is an f/5 lens. With a sensor 1/10 as large, one would need a 10mm focal length lens for the same field of view, which would need to be f/0.5 to have a 20mm aperture, if one want to produce the same background blur. It's either impossible or extremely expensive to get an f/0.5 lens.