Expense is because aluminum is more expensive to produce (Did you know it takes 10 tons of boxite to produce 1 ton of aluminum? Also, aluminum doesn't naturally form in our atmospheric pressure, so giant pressurized smelter are required for production.) and it is harder to work (This is due to the metal not having much of a liquid range in our atmosphere... It's not much harder to work with, but it's enough to raise the price.).
The reason it is so popular is that it is strong and light. It's popularity in race vehicles is because it's a sport where every single ounce must be cut in order to move the car faster... less inertia to over come. Very high end cars may even have a thinner walled drive shaft which can't be used more a a hundred times or so before.
Steel has a much higher elasticity. As such it is far better suited to the centrifugal stresses which a drive shaft sees. There is a mathematical equation for how much stress a drive shaft can take, at what speeds it is most likely to fail and serves as a guide as to how long you can expect to run it before needing to replace it (PRIOR to failure)... it has to do with the type of metal, the length of the actual shaft, the offset angle of the differential and transmission, the diameter of the shaft and the wall thickness.
If you look around, you'll find more people who've had aluminum drive shafts fail at the track than steel. There's also the unending string of complaints about all the vibration which in inherant in aluminum and even CF drive shafts.
For a daily driver, steel is the most comfortable and longer lasting bet... for a track only car, aluminum is a great choice... I just assumed your car is a daily driver, so if that's incorrect then I apologize for the false assumption.
EDIT: Ever wonder why everyone isn't making aluminum crank shafts?
