Each sort of material has its own specific pluses and minuses. And the feel of a bike using those different materials can be pretty dramatic.
Steel was the original high end racing bike and they were extremely well engineered by the mid-90's. You can hear people talking about how steel has a limited fatigue life but be that as it may, since it is EXTREMELY rare to have a frame of any material fail because of fatigue you can just assume that they never wear out.
The steel failures are in most cases from overheating and "hardening" high grade steel while brazing lugs. For this reason many frame builders that used very high grade steels would silver solder the tubes into the lugs which requires a lot less heating.
The weaknesses of bike handling of the lower grades is a "wiggle and bounce" reaction from the steel tubes bending under stress and then acting like a spring and rebounding. Reynolds tried to cure this with stronger grades while Columbus developed the SL and SLX which were thicker and so stiff that they were almost impossible to wind up to bounce. In the days when a 23 mm tire was considered monstrously large this made for a tough ride.
In the early 80's in order to lighten the bikes and yet not let them rebound all over the place they started using mild aluminum tubing. Rossin, Vitus and Allen were examples. These were lighter and rode pretty well but you couldn't do things like sprint or climb hard on them and keep control because their bending was not good for that sort of thing. Later companies started using higher and higher grades of aluminum culminating in aircraft grade. This allowed them to be very light and strong but they often also had the bending problems unless the tubes were heavier or the cross sections were very large. I think that Eddy Merckx company peaked this material with the Premium. This one made the strongest steel frames feel flexy.
Then Carbon Fiber came onto the scene after experimentations with Fiberglas failed to have any advantages. This material has had a great deal growing pains since you cannot build bicycles using any of the last century's methods. All of the thousands of years of combined experience building bicycles had to be thrown to the wind. On sure, originally you had some bicycle frames build in the older manner of lugs and straight CF tubes. These sorts of tubes are easy to make and you can in general go down to your local plastics store buy these tubes and then make up some aluminum lugs and made a workable frame. Look did a really good job of insulating the carbon from the aluminum and all of their early CF bikes are running to this day though if you didn't insolate them the least water would cause corrosion and failures.
Finally the Indian, Chinese and Taiwanese started real assembly lines for monocoque frames that didn't use lugs or any sort of thing and that could spread the loads over very wide areas and reduce peak forces instead of focusing them. When you use this construction method you can REALLY lighten the construction up.
Composites also have problems with the fact that they are fibers held together in a resin carrier. Earlier resins as were used in fiberglas composites had the property of continuing to harden over a very long period. Boat builders solved this problem by simply making the wall thicknesses so great that no matter how long it cured it always had far more strength than brittleness. But bicycle frames are light under any comparison and so they would grow brittle and the resin would fracture, breaking the carbon fiber under layer.
Various resins were tried until we presently have a thermoset resin that can but may not use a catalyst. At this point in time they seem to be very reliable. Boeing uses their entire aerodynamic sections composed of carbon fiber composites with thermoset resins. If you're afraid to ride a carbon fiber bicycle now you should be frightened into never flying again.
Advantages of carbon fiber is that it has a very low modulus of elasticity - it absorbs rather than bounces. And it has a low coefficient of expansion - it doesn't change size with even major changes in temperatures.
While you CAN find carbon fiber failures they have grown increasingly rare as the material and its production methods mature.
What is my opinion? I like the way that steel handles. But I don't like the way it bounces when you get it light. Now, with frames forks and wheels and tires you can tune the bike so that it is a very good handling bike for any particular course,
Aluminum and it's snootier cousin who is always looking down its nose at you - titanium - are in general simply so stiff that they must be tuned with tire sizes and pressures. But they are not bouncy and once tuned they are pretty good for all purposes.
Carbon fiber is presently pretty well developed. I had most of the carbon fiber Colnagos and they were mostly conventionally build using the "lug" system. Just Tuesday on a ride a friend brought his Colnago Precision which was a cyclocross bike with disk brakes but MAN - that thing was heavier than my steel Pinarello.
Now I have a middle of the line Colnago CLX 3.0 and I haven't ridden a better bike. It has every possible advantage of the composite materials though being Colnago it is a little bit heavier than it could be - 17 lbs in my XL size.
There is another material on the horizon - graphene. This makes lighter weight still possible and MUCH stronger strength. Graphene is more than 10 times stronger for its weight than steel. So when they really get to using it in composite frames you can pretty much discount them ever breaking. But that is still quite a ways off - though you can presently buy tires with Graphene armor on them to prevent punctures.
Now the most substantial difference between all of the materials is cost to the buyer. You can get a good steel bike for a reasonable price. You can get a great used steel bike for a CHEAP price off of Ebay. There was never a very large production of racing aluminum bicycles so they are a bit hard to find and medium priced when you find them. Let's face it - carbon fiber bicycles are just too damn expensive. But today more and more people are converting to it. Even those who had bad experiences with them in the past. This should help to bring the price down somewhat but that will probably take quite a bit of time because companies have to pay for equipment and engineering costs. Research and development is never cheap and companies can pull that money out of thin air.
