Suppose you and your opponent have exactly the same amount of mutalisks. What is the most effective way to micro them? Attack-move towards the enemy? Focus-fire one of his mutas?
So there are only three factors which influence Muta vs Muta battles. They are, in order of importance:
A lot of people will try to tell you that the Bounce is important, but Bounce has a Range of 3 (identical to the Muta itself) so once you get above 8-10 Mutalisks, reducing bounce damage is not practical.
Army Size is the most important part of any Mutalisk on Mutalisk contest, but not just having more than your opponent. At about 14 Mutalisk, they gain the ability to one shot opposing Mutalisks. Above this point, having all your Mutas target a single target actually results in a loss of damage. Unlike the Siege Tank, Mutalisk damage is carried by a projectile, so if the target dies before it hits, the projectile does not re-target. Thus if you have more than 14 Mutalisks, the best thing you can do is split them into groups of 14 and micro them independently.
As army size is important, keeping your Mutalisks alive is almost as important. This means backing out Mutalisks who have low hit point values. Because of the nature of the Glaive Worm bounce, this means you're going to have to pull wounded Muta back prior to getting low health (think about half). Ideally you want your opponents Mutalisks to follow this unit, as Mutalisks have to decelerate on attacking. This means chasing Mutalisks will never catch up, and become easier prey. If they don't chase then you need that Muta to almost immediately get back into the fray (the technique for this I'll describe in a second).
Focus Firing is usually a well understood concept by most players, but how it applies to Mutalisks is often unique. Ideally you want to Attack the nearest opposing Muta and then shift target his remaining Mutalisks from closest to furthest. However, Mutalisks are very quick and have the useful property that they bunch up very tightly when micro'd. You'll want to use this to your advantage to prevent your opponent from focus firing your Muta down. As Mutalisks attack they will spread out a little, so you'll have to use the time in between attacks (yeah the 1.5 game seconds), to tighten them back up. This will usually require more than one action. Make sure to hit
While Muta on Muta micro may sound intense, the period for which it matters is usually very small. As the most important aspect is army size, you should gain a slight advantage through better micro early on, which will quickly snowball. If you find yourself behind at some point, do not remain and fight, but rather quickly exit.
Ideally? Spread them out into a big circle that surrounds his mutas (so you don't get hit too much with his bounce and then converge by focus firing on his mutas, specifically targeting the weakest muta next (the one that has had the most "bounces" on him).
If your coming in a clump, do hit and run tactics and hope he can't keep up with that.
Or just run him into your queen.
Not really part of the micro but if you get into a Muta struggle with another zerg the armor upgrade is better than the damage upgrade. This is because the armor will affect all the three bounces - ie reduce the damage of each attack with three, but the damage upgrade will mostly only affect the first strike.