I've got the curse of having hyper-sharp eyesight (20/10), and for years I couldn't handle plasmas because I could ALWAYS see the pixels and the space between them. Looked like a fucking litebrite to me. I bought a DLP projector, which I still like more than most other display types, even over modern plasmas (which are far better than before), simply because the image looks very NATURAL to me - much better than the LCD projectors I've seen, and affordable too. I've worked as a colorist in film/tv, and most of us still prefer CRT for color correction, but I recently had the pleasure of checking out some of the color bays at WB and they use some incredibly fancy plasmas that really blew me away.
I think my point is that good plasmas are incredibly expensive. The cheap ones, I don't think are any better than LED TVs (most of which are not backlit as Kennith insinuated, but side-lit much like my iMac, which also has a gorgeous display), mostly for the reasons Mr. Matusov has covered.
Emissive vs filtered displays, while in theory this is a correct point regarding contrast and viewing angle, in practice, there's a point where it really doesn't matter. For example, if you're sitting more than 60 degrees to the side from dead on to the screen, your viewing experience is going to be miserable no matter what. It's going to look like garbage because you'll only be seeing a tiny sliver of a screen. Who gives a crap if the colors still look great!? In terms of contrast, our eyes automatically adjust to the brightness of what we're seeing. If a display is very bright, the iris in our eyes will shrink our pupils to let in less light and not overwhelm or rods and cones and optic nerves. When it does this, the detail in the darker parts of what we see will begin to diminish, because our eyes are letting in less light. This can get to the point where there are things on screen that you SHOULD be seeing that you're NOT seeing. Yes, there can be too much contrast and too bright of a display. In most practical settings, good quality modern LED LCD TVs perform spectacularly well, and very few people will notice any backlight bleed except perhaps in a nearly completely dark shot, in a completely dark room. The good news is, you'll see what that shot is actually OF, as opposed to wondering what you're supposed to be seeing with a Plasma as your eyes struggle to adjust from the very bright shot you saw a second before.