The flat disc is a bit more precise in determining the lighting ratio of the lamps themselves, as it reads a narrower field. It is not influenced by the other lights as much. It more truly reads just the lamps themselves, while the dome will give you a better idea of how the light is actually falling on the face. If there is flare/spill from one lamp to the area mostly lit by another lamp, the dome will read that, while the disc will not. IMO, you want to meter the flare, as it is what you will actually capture when you shoot.
In your example, to capture the lighting ratio just like you designed it so that it prints as intended at your normal printing time and filter, you would expose for the brighter lamp number two (which I would actually call lamp number one, or the main light). If you expose by pointing the lamp at the main light, then the fill light will be captured at the intended value, not too brightly, like with the averaging/toward-the-camera method.
Now, if you were stuck with a certain lighting ratio (natural light, e.g.), and you would prefer if it were less contrasty on the print than it is in reality, that is the time to either average down the middle or meter the darker side, and probably adjust development as well.