The answer is that any given aperture on your camera will give a much greater depth of field (DOF) than the Canon 450D at the same aperture because the sensor on your camera is much smaller than the Canon. It is so small, as are your minimum apertures, that you cannot obtain shallow DOF.
The Canon APS-C sensor is roughly 22.2mm x 14.8mm. Your S4200 sensor is 6.2mm x 4.6mm. That Canon sensor is over 11 times larger. That is also one of the reasons DLSRs are expensive.
COMPARISON: to obtain the same DOF as a Canon 450D at 50mm focal length and aperture at f/4, you need a lens of something like 15mm at f/1.2, which you don't have. For good out of focus backgrounds a portrait photographer would use a 35mm sensor camera with an 85mm f/1.4 lens, for which you to achieve with your camera requires a 16mm f/0.3.
There's lots of information around, just Google "depth of field sensor size".
To obtain the shallowest DOF you need to be using maximum telephoto and minimum aperture, and then your subject (in focus point) needs to be very close to you... a few metres away at most for noticeable results. These are the key elements affect DOF with a given sensor size. The closer the better. In short though, your cameras are not capable of obtaining shallow DOF. It is not an issue of there being a variable ND filter - it's also highly unlikely it uses that sort of technology as well given normal aperture mechanisms are very cheap and work perfectly well.
Hope that helps.
