Wlutke, that’s sort of correct, but I would put it somewhat differently. In a good design an XLR cable will be provided with inverted and non-inverted signals, as you indicated, and those signals will be received a differential receiver circuit which responds to the instantaneous **difference** between the voltages of the two signals. Since the two signal wires in a properly designed XLR cable are twisted together, and the circuits they are connected to cause (or at least should cause) them to have equal impedances relative to ground, induced noise will be essentially identical in the two runs, and therefore there will be little or no difference between them, in terms of noise, for the differential receiver circuit to respond to.
In many designs it is also the case that the amplitude of each of the two signals in a balanced interconnection has the same amplitude as the single signal in an unbalanced RCA interconnection. In such a case the instantaneous difference in the amplitude received by a differential receiver circuit via an XLR connection will be twice the amplitude that would be received from a single-ended signal, resulting in the 6 dB difference in overall system gain that you referred to (assuming everything else is equal, including the setting of the volume control).
There are some lesser designs, however, which provide XLR connectors simply as a convenience feature, and provide that connector with just a single-ended signal and a ground. Also, in cases where a differential pair of signals is provided and received, the quality of the differential driver and receiver circuits may be less than optimal in some cases, and an RCA connection might provide superior results in those cases.
Regarding the grounding scheme, as indicated in the Rane application note which Atmasphere referred to in one of his posts dated 3-1-2018, ideally the shield of an XLR cable should be connected via pin 1 of the connector at each end to the chassis of the connected component. However for whatever reason many designs connect the shield via pin 1 to signal/circuit ground instead, which depending on other aspects of the design can result in some fraction of the signal current being conducted via the shield, in turn increasing sensitivity to cable differences as Ralph explained.
Regards,
-- Al
