Advantages of a high setting
It makes it easier to track a moving enemy in close combat.
You can turn around quickly when you have an enemy behind you.
With a weapon like the shotgun, you can easily shoot down the driver of a fast- and close-moving vehicle (such as when jumping over a Ghost and firing straight down on the driver).
In Halo 2, due to its enormous auto-aim, sweep-sniping (the act of moving the reticule of the Sniper Rifle across an opponent's head to get an instant head shot) will benefit greatly from an increase in sensitivity. This trick also works well with the Battle Rifle.
It will give you a lengthy advantage over players with lower settings because you can turn faster than them.
When charging an enemy, you can jump over them, quickly turn around, and melee them for an easy assassination.
Face Painting is applied more.
edit Advantages of a low setting
Aiming while sniping is more precise.
Players get more control over precision weapons in general, like the Battle Rifle and the Covenant Carbine.
In Halo 2, any sensitivity above 5 will decrease the accuracy of the Battle Rifle and Sniper, as the auto-aim will stop working if a player moves their reticule too fast.