The biggest reason for difference in the two lenses is aperture. The 80-200mm is a constant f/2.8 throughout the focal range and the 18-200mm varies from f/3.5 to f/5.6, so substantially slower, especially at the far end. All this really means is that the 80-200 can let in more light at the same focal length over the other.
Also, generally, zooms with constant apertures are higher grade lenses. I hesitate to make this statement a truism, but it pretty much is. Consumer grade lenses are often massive zoom ranges with variable aperture whereas more professional grade variants are smaller zoom ranges and constant apertures. The professional variants tend to be fast, sharper, and better built. There are exceptions, but this is generally the case regardless of brand.
So, that is why you might make the choice of the 80-200mm lens. I made such a choice with a Pentax variant not so long ago...
To answer your other question, I would probably recommend the super zoom (18-200) for a newcomer if you want a single, general purpose, lens. I would expect the 80-200 to be optically superior, but also more expensive, and it would probably mean a second, equally expensive, lens to fill in the range. Worth it to some of us, but not for everyone.