I don't know the actual scientific results as to which one is stiffer or not. But the carbon fiber barrels exhibit different group patterns than a traditional steel barrel does. I have 2 carbon fiber barrels in for load work up right now, and I will plan to use them as an example later. But generally, the carbon fiber barrels have a larger sweet spot, or accuracy node, than a steel barrel does (non bull barrel steel barrel).
Take this target below. The target I'm referencing is the bottom target. It was shot with a heavier target barrel in 6.5x284 with a 140 grain bullet. Load D has 4 rounds in the same hole and 1 flier, but this is obviously the best load. Now look at load C and E, which are just before and after the sweet spot load D. The groups are open and stringing a little. Now on a carbon barrel, the loads around the sweet spot load are also generally tight, and do not show near the openness or stringing patterns in the groups. So, what causes this difference? Is the carbon barrel more stiff than a traditional barrel? I don't know. But what I do know is that the carbon barrels exhibit less harmonics, or barrel vibration, that causes the groups to open up. I'll try to provide some targets later of the carbon load work-up once I have shot the rifles.