It’s much more than just what they’re made of that determines how they ride, geometry, design and material grades can all make a difference too (as can most likely, many other things!)…
But as a general rule of thumb, the following applies…
Steel – Heaviest of the materials, easiest to work with, has a “lively” character (as long as not too much of it is used) and should last a long time.
Alu – Quite a bit lighter than steel, can be shaped and formed into pretty much any shape you like these days to add strength and reduce weight. Not very lively unlike steel, can feel a bit dead or harsh to ride in comparison with steel.
Carbon – Lighter again (in general), you can make absolutely any shape you want out of it, but it’s quite a bit more expensive than aluminium or steel. To ride, carbon is not as lively as steel, it can feel like it’s absorbing the edge off some of the smaller bumps (a good thing or a bad thing, depending on your viewpoint, but why it’s used extensively on road bikes these days).
And then there’s Titanium – Most expensive of all the materials, generally frames are built around the same weight, or slightly lighter than alloy frames. Titanium is not so easy to work with, hence more conventional tubed frames are more common. Ride wise, it is best described as being more lively than steel, titanium has so much inherent flex in it that if not enough material is used in a frame, it can visibly flex quite a lot (though it probably still won’t break). Some find it too flexy, some love the way it rides.
Personally, I prefer steel. I’ve ridden a number of each type of frame, and steel still wins out for me despite being the heaviest. But I’m not an XC racer though, so weight isn’t so important to me.
Geometry and fit of a bike is probably more important than the frame material though, something to get right at purchase time. And the ability to run a big volume, fast rolling, preferably tubeless tyre in the back of a frame, can dampen even the harshest of alloy frames down noticably.
