Firstly, you'll hear many a things about material durability.
All of them have their strengths and weaknesses.
Carbon is easily the strongest. EASILY. But in a crash, I'd be wary of riding it again without having it inspected fully by a professional. I know people who have been KILLED by riding carbon bicycles that had some sort of structural compromise that wasn't inspected properly, and their bicycles folded up on them at the worst possible moment. Granted... that's a rather extreme circumstance.
Aluminum is great because it doesn't rust, and it's strong and lightweight... you'll notice this by standing on top of an empty pop can and noting that it will support your weight easily. But once someone dents the side, it will instantly crumple.
Steel is the heaviest, it rusts, and is generally mushier. But it's a little more resilliant. That should be read as forgiving. Steel is a workable metal. So you can bend things back and ride with some damage that would compromise another frame type (generally). Though I wouldn't really ride a frame that is dented, because steel is just as susceptable to folding up on you that aluminum is.
What I would suggest is... reading THIS article:
http://sheldonbrown.com/frame-materials.html (also available in our resource thread btw) read it THOROUGHLY and COMPLETELY and UNDERSTAND that Sheldon Brown is regarded almost unanimously as THE authority on bicycles. There are a couple more articles at the end of that one. I suggest looking through those as well.
In short... once you realize that your biggest concern should be finding a bicycle with the correct geometry for your purpose. You'll end up with a bicycle that fits you, is comfortable, compliant when it needs to be, yet sharp when it needs to be. I can tell you that the BEST bicycle that I have EVER ridden was a hydroformed aluminum bicycle (read: generally stiff and painful (you'll know better if you read that article I posted)) and it was EASILY by far and away the BEST bicycle frame I have ever owned. In fact, even though I crashed very badly and wrecked the from completely, I still keep the frame. I'm hoping that someday someone will invent some technological wonder that can repair it
.
Seriously though. The FRAME is the most important piece of the puzzle. Material is only one VERY small component of the process. If you get a frame that is designed properly for YOU, you'll find a bike you'll have forever. I can tell you that I'm still looking for such a bicycle and I'm no rookie either. I've owned (off the top of my head) 11 bicycles since that one amazing bicycle (1999 Marin Juniper Trail in case you were wondering) in all materials except carbon (though I've ridden a few carbon bikes), and I'm STILL looking for something that is even half as close to perfect as that one was.
Ask more questions... I'm bored and am unemployed.