Active matrix displays have sharper images, purer colors, better contrast, and wider viewing angles than passive matrix screens. In addition, there is no "trailing" effect in active screens. Ever wonder why the "mouse trailing" was an option on earlier laptops? To disguise the trailing on the screen!
Technically, I think it has to do with the fact that active matrix screens lights all the pixels on the screen at one time, frame for frame. Passive matrix screens do not; they only light one pixel at a time and "scan" down the screen, like a CRT. CRT's can get away with scanning much better than LCD's.
Fyre4ce