If I'm wrong, I hope someone will correct me, but here's what I understand about it:
Each object that's hit by light, reflects that light in all directions. Your camera lens captures some of that light, but it contains rays which were sent out at slightly different directions (the light hitting the right hand side of the lens must have been reflected off the subject in a slightly different direction than the light hitting the left hand side of the lens). The lens bends the light rays back to a single point, right at the sensor, which is then in focus.
Out of focus (OOF) areas of the photo occur when the rays of light from a place closer to, or further from the subject, hit the outer edge of the lens at a different angle compared to those rays of lights that are reflected off the subject. Because the lens bends light in a single way, rays coming in at a different angle will not come together (be focused) at the sensor, but slightly before or after it. At the sensor, these rays of lights will cover a larger area, causing the unsharpness.
The DOF is therefore caused by the 2 factors which determine the angle at which rays of light arrive at the sensor: the distance to the subject (closer by = steeper angles = shallower DOF) and the physical size (diameter) of the diaphragm / aperture (larger diaphragm = steeper angles = shallower DOF).
Bigger sensors don't necessarily have shallower DOF, but to get the same field of view, they need larger lenses (the X10 only requires a ~6mm lens to get the same 28mm equivalent field of view as a 14mm lens on m4/3). Since the f-number of your aperture is calculated as "focal length in mm divided by physical aperture diameter in mm", an X10's 6mm lens at f2 has a physical aperture size of 6/2 = 3mm, whereas an m4/3's 14mm lens at f2 would have a physical aperture size of 14/2=7mm. Therefore, despite the fact that they have the same 28mm-equivalent field of view, the M4/3's real aperture is more than twice as large = steeper angles for the rays of light falling on the sensor = shallower DOF.
Making the effect you're seeing even stronger, the 50mm f1.8 lens has a 27,7mm aperture, which is about 10 times as large as your X10's at 6mm / f2.
sorry it turned out to be such a long read!