By “normal display” I assume that you mean the traditional cathode ray tube (CRT) screen.

No CRT TV is capable of showing HD pictures. This is mainly because the scanning circuits were not designed with the HD standards in mind. They don't have the correct input devices and the circuitry is not designed to handle digital signals.

Also, very-very few CRT screens have the resolution required for HD anyway. The ideal top of the range CRT personal Monitors could do it if you feed them from a HD specification picture via a DVI input.

Modern LCD/plasma screens are designed specifically for HD use (720/1080). They only show standard definition (625 line) photos because the electronics optimise the “scan” to make it work.

Therefore it means that modern flat panels can not be as good as the Ideal of the CRT sets with SD photos. But the Ideal flat panel sets are far superior than the majority (mediocre) of the old CRT sets.

This is one reason why it is a bad investment to buy Cheap plasma/LCD televisions. The electronics don't do such a good job of showing SD photos. You get “artifacts” such as poor colour range, lack of definition and parts of people's faces appearing to move independently of the rest of their head etc.

Answer:
Sending a HD display to a non-HD TV is useless, it will either display nothing or down-convert the picture to 480i (SD). An SD picture on an HD TV can look reasonably good (but nowhere near as good as HD); as long as you're not standing very close to the Television. From the other side of the room it's harder to tell the difference even on our 60″ pioneer kuro.
Answer:
I guess it would depend on the sizes of the displays. If you’ve a 27″ standard tv with SD cable, or a 47″ LCD with SD cable then the 27″ might look more crisp.

I would still take the more massive display even though it might not be as sharp looking.

Answer:
An HD display, even without an HD signal has more pixels and will give you a better picture even from a non HD source.
Answer:
A “normal display” with a HD signal is useless because it can’t process it.