Right then, time for my five penneth, it's like two penneth, but more...
1. Carbon wheels will be new, new = faster! proven by research
2. Likely that carbon wheels will be more expensive, expensive = faster (even if in truth they are slower)
3. Carbon are more likely to be aero, aero = cool + a nicer noise
4. Carbon wheels look better. I will forgive Andrew as he hasn't seen the difference between my bike from alu wheels to carbon wheels. That is my fault for only going on moist or wet rides with him and using the other bike.
5. Rotational mass. I will stumble into this one with a little past experience. My previous track car was a Caterham R500, it weighted in with about half a tank of fuel at 480kgs. The difference between the magnesium wheels and light slick tyres vs. standard wheels or even mag wheels with non light tyres was immense. Bearing in mind this car was light and had a genuine power to weight of 500bhp / tonne, you could very much tell the difference.
Rotation mass does matter, the lighter the better. A lighter overall weight will make getting up hills easier, but having lighter wheels to achieve this, will also make accelerating take less power and overall any change in momentum.
Even better if the carbon, lighter wheels are aero, as being aero they will take less power to maintain at speed.
A light non aero wheel out to take the same power to maintain as an identically shaped but heavier non aero wheel. But the advantages of the light wheel is the easier change in momentum, accelerating and braking. The heavy wheel will have more momentumn, so in theory will slow down lass quickly, but I don't necessarily see that as an advantage, especially if they take the same power to maintain at any given speed.
A light aero carbon wheel will take less power to change momentum i.e. accelerate, but will also take less power to maintain due to the aero advantages. Light and aero beats light and not aero. And light and non aero beats heavy and non aero.
That's my five penneth and some of it has even been scientifically proven...
If you are just going alongside flat at the same speed always, weight of wheels makes no difference, only aero will make a difference, but if you encounter any gradient or need to brake or accelerate then lighter comes into play, along with aero.