The first thing to note is that with those numbers (and what all the DoF calculators all say), the smaller sensor actually has the smaller DoF. For most people that is quite a surprise because they have all been told that bigger sensors have a shallow DoF but the DoF calculators clearly show otherwise! Some people would swear you are living if you say that!
The DoF calculators take into account the circle of confusion. This is a much more complex concept and relates to the pixel density of the sensor, the final print size, viewing distance, lens optical characteristics also how good your vision is. The DoF calculators make some educated guess at what threshold one would deem sharp and at what would be soft- the DoF is the distance between the near and far sharpness limits. But these limits are not black and white and also depend on how big you view the final image. Furthermore, as the distance increases or the focal length increase the importance of the circle of confusion becomes less important.
Ultimately it is complexity you can do without. When you view the image image at the same size and below the circle of confusion limit of the smaller sensor, DoF is not strongly proportional to sensor size (and if it is the theory actually states the smaller sensor has the smaller DoF) and everything I said holds true. The reason I say to ignore the circle of confusion is it only has a small part to play and is dwarfed by other erros. For example, that f/1.8 lens might actually be closer to f/1.9, and those 50mm might really be 47mm (and 44mm when focused closely). The manuf a true round down/up to the nearest common unit that makes their lens sound better.
The true math behind DoF and circle of confusion is quite daunting, what I presented is a summary that is physically correct simplification that is more intuitive.
http://en.m.wikipedia.org/wiki/Depth_of_field
http://en.m.wikipedia.org/wiki/Circle_of_confusion
What a larger sensor is allowing you to do is capture more detail which can be enlarged to a bigger size (or conversely, if you enlarged the image size by a constant factor of 100 the bigger sensor will enlarge to a bigger size). If you display the image bigger then what you perceive to be sharp is reduced, and that reduced the apparent DoF, so the smaller sensor seems to yield a shallow DoF, contrasty to what some would lead you to believe.
Confused? Well, you know sometimes you have a photo that looks sharp on the LCD screen but when you zoom in on your monitor at home it looks soft, that is related to circle of confusion. If you enlarge the image enough then you see different sharpness or softness. Bigger sensors allow capturing more detail that be viewed bigger. If you view it bigger then the visual DoF changes.
Another analogy is when you have a shallow DoF photo where the background is all blurred. If you view a small thumbnail of the photo the background looks sharp.
In the real world the circle of confusion just isn't important unless you print as large as you can possibly can (and in which case, smaller sensors have a smaller DoF), ergo the difference in sensor size again doesn't affect the DoF directly, but indirectly and in a way that you might not expect.
In summary, a larger sensor has a wider field of view for a given lens, can capture more detail, is better in low light, and can make it easier to capture a shallower depth of focus by letting you get closer or use longer lenses. The take home message is a bigger sensor makes it easier to capture a shallower DoF, for the most part it doesn't do that directly (and in reality actually increases DoF under constant conditions). It is quite obvious to me that a larger sensor captures a wider field of view and when making adjustments for that you change the DoF. The circle of confusion can be ignored and thus any differences in the sensor it self ignored. If you are determined to believe the sensor makes a difference then the truth is the smaller sensors have a smaller a DoF.