I have noticed the same thing in viewing the one image over a range of monitors or displays. Colors will manifest differently as well as monitors are often calibrated different from one another, if at all.

My first guess is that it is that the posterization you are seeing is more of a factor of the tonal range or some characteristic of your monitor rather than the image it is trying to display. In not knowing much about how monitors and displays work, I suspect that they have some sort of range limit or built in tonal compression of sorts as a matter of efficiency or expense saving, but that is a wild guess really. It could also be a factor of dot pitch.

With regard to differences between computer based viewing and printing, bear in mind that monitors can only display 72 or 96 pixels per inch where as you would need to start at about 300dpi for a decent print.

I have never noticed or had a problem with posterization in any of my prints, but then I don't tend to manipulate curves much if at all and I always print at maximum resolution for the desired print size.

I have however had a problem when creating graphics and effects that feature some sort of a faded appearance or graduated color effect. I used to use a program called Fireworks for web based and printing image manipulation and if I exported an image at a fairly low resolution I would get fairly obvious posterization, particularly in printed form. Very similar to what is shown here: