Lighter and stronger are the real gains. Also there is coolness factor. In a rare move I wish to cite for points 1 + 2:
Look, who has the longest unbroken history of carbon fiber frame making in pro road racing, uses the tapered fork steerer design to eliminate the narrow waist at the junction of the fork crown and steerer. This allows their all-carbon HSC6 fork to be laid up as one unit and in a manner that keeps the unidirectional carbon filaments that support the structure flowing from the fork legs, through the crown and up the steerer tube in a smooth, unwrinkled matrix. The more uniformly that the fibers are aligned where the crown flows into the steerer tube, the stronger the fork will be in its most highly stressed area.
Look’s engineers also developed a tapered lower bearing interface that eliminates the stress concentration that a conventional notched-type crown race would cause. The bottom line for tapered road steerers is that, done correctly, it streamlines the manufacturing process and makes for a better one-piece carbon fiber fork.