I've got a steel Giro 26 and a carbon fiber CA2.0.
The CA2.0 is plenty stiff, at least in terms of torsion when pedaling. The choice of tire size does affect the ride quality. I've got a 650C wheelset and a 26" wheelset. The 26" wheels can take a bit larger tire, which handles rough roads better.

To me, the biggest difference is the seat. The Giro has the mesh seat with the thick pad for the bottom. The seat structure isn't very stiff laterally, and the bike seems fairly flexible and squirrely.
By comparison, the carbon seat pan and thin foam pad is mounted solidly to the frame. It feels much stiffer in regards to control and bike handling.
I've had both bikes for over 10 years, and have forgotten a lot of the terminology for the seat types... sorry!

Steve in Peoria