Racing
Road racing cycles are generally out and out performance cycles, always with a degree of comfort, carbon fibre and titanium are most common on racing frames due to their low weight and rigidity whilst being relatively comfortable. Steel and Aluminium Alloy 
race frames are still about although steel is making a bit of a resurgance, aluminium frames are only used more as an evtry level frame.
Road racing frames are built to be as responsive as possible and do not have any provisions for mudguards, the chainstays are as short as possible to ensure as much power is transferred from the pedals to the rear wheel.
Carbon fibre frames can be all types of shapes, some of it due to rigidity some of it due to aerodynamics, and some of it usually a bit more than we would like down to style, due to the damping effects of carbon there are very rarely issues with the frame being too harsh, steel and titanium on the other hand get harsher as they get more rigid. Aluminium even more so. The benefits of steel and titanium over carbon fibre is their resistance to damage and reduced loss of integrity if are damaged.
