I own both of these cameras. The F801/N8008 cameras are much better built, and take normal, inexpensive AA batteries. The autofocus is decent but not super fast. Then again for most subjects, AF speed is not all that important. Accuracy is excellent, especially with faster lenses.
The F80/N80 has significantly faster autofocus and more convenient autofocus, since it has multiple sensors (five compared to one, if I recall correctly). However, I'm not sure I'd term it more accurate.
One other advantage of the F801/N8008 bodies is that they meter with AI and newer manual focus lenses. The F80/N80 needs electronic contacts on the lens to permit metering.
Personally, if I were to only own one of these I'd buy the F801s (which boasts AF tracking and faster AF than the original F801) and enjoy the higher build quality and extra features.
As posted above, the F90/F90x is a terrific bargain and has faster autofocus, with a larger sensor, than the F801/N8008 series cameras and it is not much more expensive . The F90 (non-x) and its US equivalent, the N90 (non-s) is a particularly good bargain if you can live with 3.6 fps rather than the 4.3 fps of its replacement.