Rafael, I will give it a shot. One immediate advantage of fully differential circuits over single-ended is noise rejection, noise rejection from the power supply, and noise rejection from the input.
Power supply noise that is common to both halves of the differential amplifier is rejected by a ratio, usually measured in db; rejection ratios can be easily over 100db. Common Mode Rejection Ratio (CCMR) is the ratio of noise rejection at the inputs: differential amplifiers only amplify what is *different* between their inputs (inverting and non-inverting), so what we are talking about here is if you have the same signal on both inputs, how much of it will get amplified. It is not uncommon to see CCMR specs of -95db or more. In real world terms that means you could have a 25 run of unshielded wires attached to both inputs and hang on to them with your fingers, and basically not hear a thing through the speakers.
The result is that it is possible to build a quieter circuit with less stages of gain overall. This, despite the fact that differential circuits *have less gain* than the equivalent single ended circuit!
A differential amplifier in theory has 6db less noise per stage of gain as opposed to SE. The parts count tends to be between 25% to 50% higher depending on execution. The types of parts involved, a few resistors and an extra gain device like a transistor or tube section, are not significantly more expensive. If you want to do differential right, what *can* be more expensive is the power supply, as it is helpful to have a bipolor supply with equal plus and minus voltages. This is not a significant transformer cost as it does not require more windings or more current, but it does mean the addition of more power supply rectifiers and another set of filter caps (and regulation if applied).
So the cost of execution winds up only being about 20-25% higher overall, as the chassis and transformer(s) are the primary costs in most audio products and a sort of common denominator.
If your circuit is fully differential throughout, an interesting thing can be observed: since noise is theoretically 6 db lower per stage of gain, the more stages you have, the more pronounced this effect is. In practice, you may not get the full 6 db, so for example in our MP-1, which has a total of three stages of gain from MC phono input to line output, and if we assume less than optimal noise concerns, it will still be a good 12 db quieter than the same circuitry executed single-ended. That fact alone, especially for phono users, should carry some weight.
The idea that you can have less stages of gain means a simpler signal path overall; quite the opposite of the usual assumption of a more complex signal path.
To put this a little clearer: with proper execution, a fully differential preamp or amp will have a simpler signal path than many single-ended counterparts. The bottom line is lower noise and a simpler signal path, for a slight increase in cost.