When I pass through the G-System, the level drops down. This is true if I use it in front of my amp, or if I connect through the FX loop of my amp with the 4 cables method.
This is due to the BOOST function attenuation. A boost in the digital world is only possible if you do not already operate at maximum level. A boost therefore derives from releasing an attenuation (ie. turning the level down). On the G-System, the output is by default decreased with 6dB. So the level is 6 dB lower than the input level. If you want to adjust your levels with your amp input /or return, you should press the boost button.
If you don't need the boost function you can set the boost max to 0dB in the Global Levels menu.