OK - I've lost count of the times I've made this post on various car forums, but here goes again.
There is no such thing as an interlaced image on an LCD or plasma screen. These TVs are, quite simply, progressive by nature. Because this type of screen has fixed pixels, there is no form of scanning involved (as with CRT), and therefore you don't need to draw alternate lines from the top left to bottom right.
What actually happens when you feed an LCD or plasma with a 1080i image, is that it marries up each half of each frame and displays them as a single, whole frame.
HOWEVER - and this is the important part - if you feed your TV a 50Hz 1080i signal, you will basically be viewing a 25Hz 1080p image, because each one of those 50 frames per second is only half a frame. If you're watching a 1080p 50Hz feed (on a compliant TV of course) you're getting 50 frames per second - the result being smoother motion etc.
HOWEVER - yes there's another however - the pinacle of image quality isn't just 1080p, it's 1080p 24Hz. This is because movies are shot at 24fps, so if your TV can accept a 1080p 24Hz signal, it means that no post processing nonsense has been applied to the film - anyone who understands what 3:2 pulldown is will know that this is very good news, and anyone who doesn't, I'm afraid it would take me most of the night to explain.
Now some of you are probably thinking that 24fps isn't going to look particularly smooth, and you'd be right. This is why most modern TVs will apply some kind of even pulldown technique to compensate - this can be anything from 3:3 up to 5:5 pulldown. This basically means that each frame is repeated several times a second to appear smooth to the human eye, but because none of the frames are being altered in any way (as they are using 3:2 pulldown), there's no degredation in image quality. Hence a 1080p 24Hz source with 5:5 pulldown applied, will result in a 1080p 120Hz picture.
To address another point made above - yes, the larger the screen, the more beneficial a full 1,920 x 1,080 panel is, but that doesn't mean that a smaller screen won't still look better with a full HD panel. Basically, a full HD screen with 1:1 pixel mapping is displaying each and every pixel of the source exactly as it should be, with no need for scaling. This method will always produce a sharper picture, with everything else being equal.
It is however worth remembering that resolution is only one asptect of image quality, and actually not the most important by any stretch. For me, nothing is more important than good black level response, which is why I'd take a 1,024 x 768 8th gen Pioneer Kuro over almost any full HD LCD screen. Luckily I have a full HD 9th gen 50in Kuro now, which is, quite simply, the best TV on the planet right now.
Another majorly important aspect is picture processing, which is why you pay more for a TV from the likes of Philips, Panasonic, Pioneer, Sony etc. Far cheaper TVs will have similar specs, but won't have anywhere near as good picture processing, which usually results in standard definition looking terrible - which unfortunately, is what you'll still be watching a lot of the time.
Hope that's useful