The primary differences are with the additional fine-tuning advanced settings of which the 800 has the upper-hand. The 800 also has a Gold Detect Mode that the 600 lacks. The 800 can also use 20 kHz and 40 kHz singly whereas the 600 incorporates both frequencies in multi-IQ mode.
The 800 comes with wireless headphones the WM 08 module whereas the 600 comes with wired headphones. It is appropriate to note that the 600 is compatible with the same wireless headphone technology as the 800.
For most hobbyists, the 600 will provide more than excellent performance. The 800 would be better suited to the rare gold prospectors looking for extra performance when it comes to finding nuggets.