Why does a draw go farther than a slice?

A draw usually has a lower trajectory so you get more roll once the ball hits the ground.

"Draw" and "slice" are not mirror Golf shots. For a right handed golfer, a draw moves gently from right to left, a hook moves severely from right to left, and a fade moves gently from left to right, a slice moves severely from left to right. A draw tends to have over-spin, which will cause it to run, where a fade tends to have backspin and lands "soft".