Besides looks cool as hell. How many people can do that acrobatic at his speed....not too many people.
He's also clocked at the fastest guitarist in the world. Although in his songs he never shows his fulll speed. He saves that for his live solos. (YES! He is faster than Buckethead....although one has to wonder if buckethead is really Angelo...hehehe)
I started learning guitar because of Randy Rhoads..but Yngwie J. Malmsteen is my biggest influence.