Doubt

Resolution – means the level of detail of a picture or video and the level of detail a television or computer screen can display. Every picture is made from thousands of tiny points called pixel and every pixel has its own colour and a different intensity (that is how strong the colour glows). Those pixels build horizontal and vertical lines like a raster; the higher the resolution the more pixels a picture has and the more details can be displayed.
Higher resolution gives higher crispness, better image stability and better colours; ergo the higher the resolution the better is the picture.

In movie information or on DVD’s usually only the vertical figure is shown:

480p = 704 pixels horizontally and 480 vertically
720p = 1280 pixels horizontally and 720 pixels vertically
1080p = 1920 pixels horizontally and 1080 pixels vertically

Let’s presume you have a 38” screen, capable of displaying 720p. A low resolution movie, e.g. 480x272 will have to be ‘stretched’ because it does not provide enough pixel/information to fill your TV’s 1280x720. To make it more obvious: 480x272 = 130.560 pixel per inch (measured in dots per inch, dpi) and 1280x720 = 921.600 pixel, so there are 791.040 pixel missing to be filled at every inch of your screen, about 6 times more information would be needed to do that and about 15 times more if you have a 1080 HDTV (1920x1080 = 2.073.600). But your screen cannot leave those missing pixels blank, so it stretches the ones available by 6 or 15 times for our example. The effect is less noticeable on smaller screens like 17” monitors and much more dramatic on bigger screens like 50” 1080p or above.

If you have a low resolution TV like a 640x480 standard TV you might be happy with similar resolution encodes and you can benefit from the smaller file sizes they usually come in.
If you are looking for higher quality and/or you have a larger screen, well you might want to go with the larger files with higher resolution. The best HD quality if file size is a concern is to use 720p encodes with high bitrate and high frame rate with a 720p high Mhz HDTV with a screen 42" or smaller (according to the experts).

Other things such as contrast ratio, colour saturation and colour accuracy are more important to the quality of a good encode. Also the bit rate is crucial, and should be the higher the faster the picture moves e.g. in an action movie with very fast moving pictures.

Resolution comes in at a distance, relative of course, within its standards. Meaning that there is not much of a difference between a very good 720p and a good 1080p encode or between a very good 512x384 and a good 720x400. But of course the world between a 400x272 and a 1920x1080, even if the first is very good and the latter ‘just’good.

Hope it helps