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There's a difference between weight weenie carbon and using carbon to improve ride feel and aerodynamics. I've got an old bike made out of Reynolds 853 steel that's lighter than my recent vintage full carbon bike.
The "ride feel" argument is something I quite frankly never understood. I guess it's because I don't do competitive road racing (more of an ultra / bikepacking sort of guy). When I was shopping for my current frame (Kona Rove), I picked up the steel version mostly for maintenance / mechanical reasons more than anything else. Don't see much of a difference in "feel" from my old aluminium road to be honest (other than…
Also the feeling is subtle enough that the components on your bike can be the larger factor. Tires, crank arms, handlebars, tire pressure, etc.. will all play a factor. Swapping all of your components from one bike to the other would be the best test, but unless your components in aggregate provide a "neutral" feel, it is possible that they could overwhelm the feeling that a different frame will provide.