Warning: SPOILERS through The Flash #49
The official answer to this question has changed repeatedly since the two heroes first raced around the world for charity in Superman #199 in 1967. The two heroes have raced several times since then, in the comics, cartoons and movies. As a general rule, the comics claim that The Flash is the faster hero, with Barry Allen, Wally West and even an octogenarian Jay Garrick having outrun Superman over the years. Other media tend to portray Superman as the fastest, with the Justice League movie showing Superman being able to see The Flash coming and countering his super-fast attacks.
The Flash #49 sees Barry Allen and Wally West engaged in a high-speed chase that threatens to destroy the Earth, as the shockwaves through The Speed Force begin to affect other aspects of reality. In order to stop Amanda Waller and ARGUS from enacting a lethal sanction against them, the Justice League and the Titans move to stop the two speedsters.
This leads to Superman flying after both Flashes, in an effort to find out what has them so stirred up that they're moving so quickly.
Within a few seconds, Superman returns to his allies and the ARGUS group under Amanda Waller's command. Shockingly, Superman is out of breath and panting, having to take a moment to compose himself before he can speak. His hair also appears disheveled and his face is flushed and sweaty. Finally, Superman gasps that he was unable to get close enough to The Flashes for them to hear him and admits that he couldn't catch up to them.
While this story is unlikely to dissuade those Superman fans who insist that he is the most powerful superhero in the universe in every arena and "can do anything," as in the song by R.E.M., it does put another feather in the cowls of both Barry Allen and Wally West. It remains to be seen which version of The Flash will prove to be the true Fastest Man Alive - a question that will surely be answered as the Flash War event continues.
The Flash #49 is now available from DC Comics.