I, too, went the LCD route initially because I thought the burn-in issue was important enough to go that route, but ended up exchanging the LED-LCD I bought for a plasma and was much happier.

I have my plasma TV set to automatically shut off after 3 hours of inactivity. Also, I have the "pixel orbiter" feature turned on which periodically slightly shifts the picture around (not noticeable to the human eye when it happens).

From what I have heard (in places like avsforums and elsewhere), newer plasma TVs are much harder to permanently burn, especially after the initial break-in period; it is pretty much a thing of the past. You'd really have to try really hard to make it happen (leave it on a still image for more than several days), and I think an auto-shutoff of 3 hrs will prevent that. I don't have any scientific data to prove this, though.

I haven't been a long-term owner of a plasma TV yet (bought my first HDTV set about a year ago), so I'm not a good data point, but in that year I have not experienced any such problems and we leave things paused or on menus all the time. I expect that some day my plasma display will show signs of age. Supposedly, the green phosphors tend to age faster than the blue and red, which will cause a shift in color. But that could be 10 to 20 years from now. And LCD is not immune to aging; the 9-year-old LCD monitor I am using right now has had uneven brightness all over the screen in weird blotches for the last several years. I assume its a backlighting problem; but it doesn't bother me as I've adjusted to it and I continue to use it. If my plasma ever develops burn-in, I'll probably adjust to it in the same way.

The difference between LCD and plasma for me is this: with LCD I find myself noticing all the artifacts -- the colors being unrealistic, the motion blurs, the flashlight effect (backlighting being noticeable on dark scenes), etc. Processing like judder correction and blur correction just makes things worse because it makes film look like it was shot with a video camera. LED-LCD TVs are especially bad (I owned an edge-lit one for a few weeks before returning it), because the colors are even more unrealistic than with CCFL-backlit, though maybe the newer tri-color ones are better.

Whereas, with a good plasma TV I can just watch the content because there are no artifacts and deficiencies that I can see. The colors are closer to what you can expect from a CRT. Also, plasma displays seem to smooth out pixelation; I can watch video that is very low resolution and it looks great fullscreen on the plasma while it doesn't look good fullscreen either on my LCD or CRT computer monitors. I guess you can say that plasma is slightly less sharp, but this works out in its favor.

One of the big differences is: with plasma each pixel is actually producing its own light, whereas with LCD you have backlights shining through the pixels which is why LCDs are not even. Also, plasma looks the same from all angles, whereas with LCD you generally have to be center (vertically and horizontally) for the best picture, though some LCD TVs pull this off better than others. Side note: OLED displays also have each pixel producing its own light.

Maybe I am really picky (I didn't realize how picky I was until I started shopping for HDTVs last year) and the typically consumer wouldn't be as concerned and only videophiles care enough about the difference. But I think coupled with the fact that plasma TVs are generally cheaper than LCD TVs for equivalent quality and sizes, and the fact that I think with the more expensive LCD TVs you are paying for tech that is compensating for the inherent defficiencies with the technology (e.g. local dimming to make up for the lower static contrast ratio), I think plasma is the better buy for even the typical consumer.

I think the slight risks of possible plasma burn-in in the distant future are way too small to choose what I think is the less suitable technology for TV/film viewing.