Input impedance, or resistance, should typically be high: at least 10 times that of the output impedance. The reason for this is that input can overload the signal source and reduce the strength of the signal. Musicians want the timbre of their instrument to be perfect; they don't want the signal of their instrument weakened and they want to get the desired character of their instrument's sound. They will use a two-stage amplifier in their pre-amplifiers and power amplifiers for this reason.
A two-stage amplifier has reduced output resistance or impedance. Intuitively speaking, a musician wants this to be the case in order to operate the speakers of his equipment as loudly and as clearly as possible. If the output resistance is too high, the signal going through the amplifier will be too weak to drive a load (e.g., the speakers). While close to perfect instrument timbre can be achieved with increased input impedance, reduced output impedance ensures that instrument timbre can be heard across the speakers.
Increased gain or higher overall gain bandwidth is something that will make a heavy-metal guitarist smile. A two-stage amplifier will drive heavier loads (such as larger guitar amplifier speaker cabinets) with lower signal distortion. A guitar player can have a very clean guitar sound that has a good amount of gain without an unpleasantly distorted sound.
Two-stage amplifiers are more efficient in handling power than their single-stage counterparts. This means that an audio system that has a two-stage or another kind of multistage amplifier can put out more power more efficiently to drive larger loads. Power wastage as heat is reduced; for professional audio enthusiasts, this means that they can have louder sounds with less risk of damaging their equipment because of overheating. This is especially important in larger professional audio setups such as concerts that involve the use of multiple loudspeakers, mixing consoles and power amplifiers.