In theory, two transparent (a magic word of the science forum) amplifiers or signal paths should not be distinguishable.
That is when the S/N, cross talk, distortions, etc. are below the audible threshold, no difference can be perceived. It is (or can be) the case in several unbalanced vs. balanced scenarios.
In real life, there can be different situations. It may (strictly hypothetically, of course) happen that some advanced manufacturers manipulate higher harmonics for more pleasant sound (a la lamps).
Or, more realistically, balanced and unbalanced can be entirely different signal path. A notable case in hand is Fiio Q1 II, where the balanced path is much more powerful/capable and is drastically different from unbalanced (a good way to hook consumers to "balanced", worked for me...)
Then in many DAP/DAC designs, a balanced path is handled by two chips vs. one for unbalanced. Two is more than one (a simple consumer arithmetic). Also the two-chip design enables two modes: either (more common) twice higher voltage or lower S/N (so called ACG, common ground) mode. This continues to hook me into "balanced". With balanced cables of all the colours (2.5 in my case) and 2.5 to 3.5 connectors, I can use any audio orifice in my disposal and enjoy the music in all its sonic beauty