What makes skintones look green on photos?

I have a cheap compact casio camera, and while the quality is only mediocre the colors are always perfect.

Yesterday I upgraded to a high-end Sony bridge camera (HX100V) and whilst the quality is better the colors are really bad.

Almost all face shots have greenish hues in the skintones, especially around the cheeks, forehead and neck. In tungsten light skin looks orange and brown hair looks red. I have tried auto settings as well as the appropriate white-balance settings.

I have also noticed the green hue issue on my dads canon SLR, as well as a friends Nikon SLR.
And yet somehow, my cheap compact casio NEVER struggles with color.

So why is this happening? Is it just that casio have better software for white-balancing despite it's lower quality lens/sensor?

The other thing to note, is that the casio is a CCD whereas my Sony and the SLRs are all CMOS… But is this a coincidence?

Green tone is usually the result of shooting under fluorescent light, I assume you are setting the white balance to fluorescent. However, this lighting has many different values, and no one white balance setting in the camera is always going to be correct.

Setting the WB with the presets should at least get you a half way decent photo, but not always perfect. It is time for you to learn to use a white balance tool and begin shooting in RAW. You can then balance the color to perfection.

The Whibal card is the best tool I have found for this purpose.

http://www.whibalhost.com/_Tutorials/WhiBal/01/

As for the Casio, yes, it could be that the white balance settings in it may actually be better than your new camera, but that is about all that can be said for it.