Varies loads tbh, construction’s as important. You can have a relatively flexy/comfy alu frame, a stiff ti frame…
But the cliches do often bear out basically because of marketing/selection- manufacturers know comfort/flex/give sells titanium, frinstance, and people tend to expect stiff aluminium. Steel’s a bit harder because so many steel frames are basically lumps- we tend to think of the springy feel of a posh lightweight 853 number or old Kona or something but it just doesn’t apply to so many steel frames. Tube thickness I think? Whatever it was that made me love my Soul was just completely missing from my BFe. My Ragley Ti and alu Ragley Mmmbop totally fulfilled the cliches.
Carbon’s the wildcard because it can be anything you want it to be.
All in all, you’ve kind of got to ride the bike to know.