Balanced is more immune to unwanted signals (external) induced in cables and for ground loops. That is the main reason for using balanced cables.
And that's for interconnects, not headphone cables. A true balanced interconnect has 3 wires and sends + on one, - (inverse) on the second, plus the ground. "Balanced" headphone cables just give each speaker their own negative wire. This is an interesting write up on the topic:
Audio Myth - Balanced Headphone Amplifiers are Better
This Myth Goes Something Like This: "Balanced headphone amplifiers are better." "If balanced line-level connections work well, balanced headphone outputs should also work well." We disagree! Benchmark does not offer voltage-balanced headphone outputs on any of its products. The reason for this...
benchmarkmedia.com