Probably, the first thing to make clear is that an wired signal interconnection can be balanced or unbalanced, but the active electronics driving that interconnection is more properly termed differential or single-ended. Differential drive is not necessarily synonymous with balanced interconnection, and single-ended drive is not synonymous with unbalanced interconnection. The active drive electronics and the wired interconnection are separate matters. For example, an single-ended driver circuit is rather easily adapted to fully benefit from the common-mode noise rejection offered by balanced interconnection.
Objectively, an correctly implemented balanced interconnection via XLRs is the superior to unbalanced via RCAs, primarily due to it's common-mode noise rejection capability. Subjectively it may, however, be another matter. Subjective differences (in the absence of common-mode noise) are likely due to the implementation of the internal circuits of the active differential electronics.
Setting aside the benefit of common-mode noise rejection offered by balanced interconnection - which is a huge advantage if your system's environment suffers such noise - differential driver circuits can offer other advantages over an single-ended driver, such as inherent even order distortion cancellation, +3dB higher SNR, faster slew-rate and reduced signal based modulation of the power supply rail(s) compared to an equivalent SE driver circuit design. However, the best differential driver circuits will also consume twice the number of parts, and therefore twice the cost, of an equivalent SE driver circuit. As such, many commercial differential driver circuits are compromised implementations in order to save parts related cost.