The RCA signal is the same signal as the XLR. Assuming you do not have massive noise, the balanced amp still cancels common mode noise you pick up on the signal and shield.
The amp will take the difference of the + and - signals. This means you get 2x signal and 0 common noise. That is, if your signal XLR is +A and -A, then the amp will get (+A - -A) = +2A as the signal. Any common noise N will be (N - N) = 0.
One reason you might hear a difference is XLR is you get 2x the voltage. it's just louder. If you level match your speakers (i.e. with a volt meter) between the balanced and unbalanced, the difference will likely go away.
The XLR and RCA might expect difference input impedances. Some units, when they take the RCA from pin 3 use a separate driver op amp for it, some just take it straight from there.