In reality, the main difference is that the Balanced XLR connectors are a lot more secure (locking) and cooler looking than the unbalanced RCA connectors.
On the test bench, sometimes the Balanced outputs have better SNR. For example when Gene measured the Yamaha MX-A5000 Amp, the SNR @ 1w for the unbalanced was 115dBA vs. 118dBA for the balanced. However, you can't hear the difference between 115dB vs 118dB.
In the pro-audio world, balanced connectors will help reduce hum noise when using very long cable lengths. But in the consumer audio world, the cables are usually not that long.
In my own system, I use only Balanced XLR cables.
Too bad they don't make Balanced HDMI and Balanced Ethernet cables.