The ride quality and its handling has much more to do with the geometry of the bike. And with the advent of hydroforming of tubes where the cross sectional area of the tube changes and the diameter changes along the length of tube, the bike feel can be tailor made.

Steel: very good work horse can be made very light, very strong. Old fashioned but very good. Can rust over years of use. Check Luna bike with Margo. She makes custom steel and very good. (alternative to Lynsky and Ti)

Aluminum: To make aluminum frame stiffer, builders used oversized oval to make it stiffer. But the builders didn't compensate the diameter of the tube for the smaller riders, the complaint were "TOO STIFF", "IT BUZZES" for those with smaller frame. Hopefully they have learned a few things and fixed their build. Aluminum will also work harden over long hard use and will wear out. A regional racer might take 5 or so seasons to work harden an aluminum frame. That's just my guess with no data to back it up. When the metal becomes work hardened, it becomes stiffer and more brittle. more likely to have stress fractures.

Carbon: Doesn't rust, stiffness of bike can be readily designed in to be either very stiff are compliant. It will crack instead of dented when crashed. But then again if the frame is dented and out of true, the frame is lost cause.

Ti: Also doesn't rust. Some of the Ti frames have cracked. builders went to too much of an extreme and resultant bikes, though were extremely light, ended up not being very durable. For a while there were two different alloys available. First one was Ti2.5V alloy. The second one was I think Ti4.5V. The second one was much stiffer but it was also very brittle and the frames made from it cracked. My Litespeed was made with Ti2.5V alloy and its handling remained the same over 7 or 8 years of use. It was smooth, comfortable and great for road race but not so good as a crit bike. But this is because of its geometry and nothing to do with the material.

For crits, you want a bike that is very stiff to give you the necessary "explosive" acceleration and bit squirrly handling for better cornering ability. It's not for distance riding.

For road/classics, you want a bike that is bit relaxed so that your tooth filling doesn't shake loose and bit more relaxed geometry so that you don't mentally tire out over the long ride.

Best offer I can give you is get a bike that you feel comfortable riding and get a descent fit. Material is of personal preference. That's just my take after years of riding on steel, and Ti. Currently have Aluminum frame Specialized transition pro, very light, very stiff, not good for road race. Have carbon/aluminum entry level race bike. Good for road but terrible for crit. And on my trainer is a old fashioned steel double butted tubed bike.

Go for the bike you like looks wise paint scheme etc. And the feel of the ride.