How does balanced work in an amplifier? IE - compared to amplifiers that have XLR in but don't employ true balanced?A fully balanced amplifier maintains separate signal paths for each of the two input signal polarities, all the way to its output terminals. So the negative or black speaker terminal is not connected to ground as it would be in an unbalanced amplifier, and is actively driven with a signal. The signal is similar to the one on the red speaker terminal, except that it is inverted.
An amplifier that is unbalanced/single-ended internally but has a balanced (xlr) input feeds that input into a differential receiver stage that has a single-ended output. That single-ended signal is fed into the rest of the amplifier circuitry, which is unbalanced.
Re the original question, several advantages (or at least theoretical advantages) of fully balanced design have not yet been mentioned. These include cancellation of some forms of distortion that may otherwise be generated internally; and, particularly in the case of a power amplifier, lower levels of power supply-related noise. There are some others as well. See this Atmasphere white paper.
My feeling is that both single-ended internal design and single-ended interfaces are inherently compromises, assuming equal quality, starting with the fact that in nearly all modern designs that have single-ended interfaces signal returns, circuit ground, chassis ground, and ac safety ground are all common. However, there seems to be ample anecdotal evidence that in most systems and for most people the degree of that compromise is either insignificant or is overshadowed by many other variables, one of which is price.
Regards,
-- Al