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The Sharingan has many abilities, but it's main one is the ability to copy every Nin, Gen, and Tai Jutsu seen by it. This means that in every fight the Sharingan is used, the more techniques are learned. Also, this doesn't require the user to want to learn the technique. It is like a defense mechanism, which operates once the attack commences. Another of the Sharingan's abilities is seeing through illusions. For example, Bunshins, or even Kage Bunshins are no problem for the Sharingan. It can see them all as chakra sources, and only the real one looks normal.
The Byakugan gives an almost 360 degree vision and can see chakra. It cannot tell the difference between kage bunshins because the chakra is distributed evenly.