I've ridden a lot of bikes of all the different materials. I feel I am rather subjective about it and have no preference.
Steel bike people say it is so smooth... idk. It's fine, I guess.
Ti bike people say it rides like steel with the weight of carbon... idk. It's still pretty heavy
Carbon bike people say it is super light and compliant... idk. Most of them are still pretty heavy.
Aluminum bike people say it is only a few grams heavier and they save thousands... idk. I don't find that much savings.
I've never sought out a specific material when purchasing a bike. I loved high end classics, so I rode steel, I liked the look of a bare frame, so I rode Ti, I bought an entry level bike when I first got into it, so I rode aluminum, and I found killer deals on frames and rode carbon.
I haven't ever noticed the nuances of difference in ride characteristics, mostly I have noticed geometry changes from race, endurance, classic, and new bikes. I have found that I like light wheels (high engagement hubs a must on MTB but not so critical on road) and I like Ultegra/Force level or above drivetrains - the shifting is noticeably smoother and quieter (to me). Unless you're building from frame up, you can't usually buy a comparable bike in aluminum or carbon. Aluminum bikes usually get low end heavy components and wheels and carbon bikes get the nicer stuff. Usually it's cheaper to buy a carbon bike complete vs an aluminum frame and build it yourself with the good stuff.
I don't care about frame material, but I do care about good components. Usually that puts me on carbon bikes.