A quote from an AVS forum member. Saves me from typing it all.

480p looks better than 480i because most traditional video material is encoded at 480i and designed to be displayed on 480i devices. 480p only looks better when it is properly deinterlaced with the proper "pull-down" and then displayed on a 480p display device.

I guess it is better to say that 480p display devices look better than 480i display devices as they actually do show you twice the apparent resolution at any given moment due to these techniques.

Now, this falls apart with 1080i and 1080p as we are basically all using progressive (p) display devices. This is true even if your device only takes in a 1080i signal. All current technologies (with the exception of CRT) actually display a progressive signal (DLP, LCD, SXRD, DiLA, Plasma, etc.) Since this is true, they must be grabbing an interlaced signal, holding one field, combining it with the next field prior to display (this is what any progressive output device previously did before outputting the image).

The issue here is that the technology is EXTREMELY robust and that for very little cost almost all displays can do this perfectly. For film, it is trivial as there is no "time offset" between two interlaced Fields - they come from the same Frame so putting them back together is extremely simple.

You can view it as follows:

A Progressive Signal is sent as
Line 1
Line 2
Line 3
Line 4
etc.
Display

An Interlaced Signal is sent:
Line 1
Line 3
Line 5
etc.
Line 2
Line 4
Line 6
etc.
Display

In the end run the same information is in the Frame Buffer prior to display - ergo no difference.

Another point is that people continually confuse the subject when talking about 1080i and 1080p. You MUST distinguish between TRANSMISSION and DISPLAY. In your context you are talking about how the signal is TRANSMITTED as almost all of the 1080 monitors, etc. DISPLAY 1080p and can not DISPLAY in an interlaced fashion anyway.