[VinnyP]

Lenses aside (which behind the photographer make the biggest difference) the big three factors which will affect your finished image are the sensor the metering and the focus system. Both cameras share all three of these so on that basis they are the same.
However of course they are not the same, in some areas, how important that is to you is something only you can answer. The D200 has pro build quality, weather sealing and is made of stronger materials (It's also a qualifying body for NPS/NPU membership). It also has a higher frame rate so would be better for fast moving stuff and has more options to "tweak" the settings. Finally the 2 cameras will handle differently, the D80 weighs less but has less of a "pro" control layout so you will need to delve into the menus more often to adjust things again it's very much personal taste.
On most criteria if your budget stretches to either camera then the D200 would be the one to go for BUT I'll take you back to my first line. If you can get a D80 and a better lens or just the D200 9 times out of 10 the lens will make far more difference than any difference between bodies.