As I work on a new build, I'm evaluating components like handlebars, stems, seatposts, etc. A big decision is between aluminum and carbon. I'm noticing that the weights on these components are quite similar. Sometimes carbon components are even heavier. Am I to assume that these components are stiffer? What are people's experiences with carbon vs. aluminum?

Depends on the exact components in question - generalizations are meaningless. From a design standpoint, carbon has an advantage when it comes to vibration damping and the ability to tune the flexibility. Comes at a high cost though. Not worth it according to my value stream but you may differ.

Easton in particular. I understand that carbon has better damping characteristics, and that it may be tailored to be stiffer. My question is: do companies actually take advantage of these characteristics, or do they just make carbon parts because people will buy them (often at a higher cost)?

My question is: do companies actually take advantage of these characteristics, or do they just make carbon parts because people will buy them (often at a higher cost)?

Companies are always looking for ways to increase their profit margin. Carbon is the answer in the high-end bicycle world. No doubt there are functional advantages to carbon but money is the prime driver.

You can't assume anything about stiffness, based on weight. Most carbon stem are heavier and much more expensive that the best aluminum products. With handlebars, the primary advantage is the ability to mold CF into more unusual and intricate shapes. Often, CF bars are heavier. I'm currently using all CF bars, but can't say that there's much advantage since I don't find flat top or wing shaped bars to provide any comfort advantage. I spend most of my time with my hands on the brake hoods or in the hooks and very little on the tops (not even climbing mountains).

As for seatposts, I also use carbon, but part of that decision is based on the desire for a 2-bolt seat rail clamp with a 25mm setback (FSA K-force). Thomson aluminum is nicem doesn't meet my setback needs.