Pixels, and pixel count are somewhat irrelivant, as they are the product of a square. 3x the pixel count =/= 3 times the sharpness.
OK, lets put it this way, 1280x720 is able to show detail at 1.5x the vertical detail of DVD at 720x480 and 1.8x the horizontal detail. For sake of argument, lets say 720p is about 1.5x better than a really good DVD.
For 1080p, the improvement in resolution horizontally is 2.7x and 2.25x vertically so 1080p is about 2.5x better.
The horizontal difference between 720p and 1080p (1.5x) is less than the horizontal difference of 480p DVD to 720p (1.8x) and the vertical difference is about the same (1.5x increase from 480p -> 720p -> 1080p). Anyway, by those numbers, 1080p is still less of a step up from 720p than 720p is up from 480p. Not much in it, but still significant.
That does also ignore the fact that 720p encodes done with a more modern codec such as H.264 look technically better than a 480p MPEG2 typically.
For example, if I set my HD DVD player to output 480p, HD DVDs still look better than the same movie from a DVD, especially where colour is concerned.
There is much more to the quality of an image than absolute resolution. Level of compression used is also very important and a decent bit rate 720p can and often does look better than a 1080i image in the same bit rate.
No, it cannot. It can be deinterlaced, and it has to be in order to be displayed on a modern digital display, but information is always lost when dropping frames, especially when the final rate is not an even product of the original rate.
A 1080i/60 signal has not dropped any frames. It is using the same 3:2 pull-down that allowed 24 fps movies to be shown on old 60Hz NTSC displays. All 24 frames are there and they can be recovered perfectly with nothing lost.
Are you suggesting that on an equivilant size display with a native resolution of 1280x720 (which almost no 720P display is), it would be equally as sharp as a 1080P display of the same size sitting next to it?
Not at all but if you take an image which has exactly the native resolution as the picture displayed it will look sharper than having to scale an image that is non-native. Since 720p cannot be perfectly mapped onto a 1080p display it is going to look a little soft although scaler quality will have an impact on this. If a display with 1440 vertical pixels was used, then 720p may map better onto it than scaling 1080p onto it which wouldn't fit perfectly.
There is no need to attack me or my eyesight which just so you know, isn't the best in one eye since I nearly lost my sight last year through a very severely detached retina and had to go through multiple surgeries.
I'm just suggesting an experiment and a possible outcome.
I would question your vision, and playback equipment in that case.
Really. No need for that at all.