Asteroids ... have considerably more scientific value than the moon.
That's debatable, but to the extent it is true we should be sending unmanned probes to the asteroids, not expensive manned missions. Besides, manned missions really don't have much to do with science.
The moon is much more like Mars than any little near Earth asteroid. Before we go to Mars we'll need to learn how to live there for several months, and constructing a base on the moon is a great way to gain that knowledge. It's far enough away and a similar enough environment to require similar engineering solutions, but near enough to rescue the mission if something goes awry. Also, landing on and lifting off the Moon is just what we want to be good at for a manned Mars mission. The moon's gravity is about 1/6 earth, Mar's is about 1/4. The main difference is Mar's atmosphere, but we won't learn anything about landing on an atmosphered planet from an asteroid mission.
Personally I think going to Mars is going to be a hell of a tough prospect, much harder than most people think. I can imagine a future where the first successful two-year mission barely survives the ordeal and the bleakness and suffering of the explorers turns everyone off the whole idea. Probably what we need is a faster, better, cheaper propulsion system to get us there in a month or less.