Reasons why XLR interconnections can make a difference in a home audio system, compared to RCA interconnections (although depending on the specific designs that difference may or may not be for the better):
1)The configuration of the output circuit providing the signal is different, or at least should be different.
2)The configuration of the input circuit receiving the signal is different, or at least should be different (apparently it is not in the case of the OP's amp).
3)The impedance relationship between those circuits may be different.
4)Depending on the specific designs of the interface circuits in the two components susceptibility to ground loop-related high frequency noise and low frequency hum may be less in the case of XLR.
5)Depending on the specific designs of the interface circuits in the two components sensitivity to cable differences may be less in the case of XLR. See the post by Atmasphere dated 3-22-2013 near the beginning of
this thread, and his answer to my follow-up question later in the thread.
6)And of course the cable and connectors are different.
7)Note that none of the previous factors relate to whether or not the components are "fully balanced," i.e., to whether or not they have balanced internal signal paths. As alluded to in one of the previous posts, XLR interconnections are especially likely to be beneficial if the components are fully balanced.
Regards,
-- Al