According to the rulebook (pg 18), "After a ship becomes tractored, the opposing player may choose one of the following traits:"

So, just to make sure I understand, if I tractor my own ship, my opponent moves it?

In 1st Edition, the opponent of the tractored ship chooses whether and how to move it.

In 2nd Edition, according to the Rules Reference , the player who created the relevant tractor token chooses. (The basic rulebook is worded the same way as the 1st Edition rules but the Rules Reference overrides it.)

14 minutes ago, JJ48 said:

According to the rulebook (pg 18), "After a ship becomes tractored, the opposing player may choose one of the following traits:"

So, just to make sure I understand, if I tractor my own ship, my opponent moves it?

Rules Reference overides. The player who applied the token that resulted in the Tractored effect moves the ship:

http://infinitearenas.com/xw2rules/index.php?page=tractor