There are some things that you need from a good commuter bike:
- Robustness (so that you don't come late to work too often, and won't need a new frame after an accident)
- Comfort of posture (so that rides are fun)
- Efficiency (so that rides are fun and fast)
- Durability (the bike should live as long as possible with the least servicing as possible)
Carbon frames reduce weight, as are aluminum frames supposed to do, so they have a slight efficiency advantage. Let me stress, how slight this advantage is: If you weight 70kg, and your bike weights 10kg, 5kg1kg more for a steel frame would increase your total weight by just 61.25%. However, you don't need to carry that weight, the air in your tires does. The extra weight means a small increase in rolling resistance, but that is dwarfed by the air resistance anyway. I'd estimate that 5kg1kg extra weight will not decrease coasting efficiency by more than 2%0.5%. The faster you ride, the less efficiency will be lost.
So, is such a tiny increase in efficiency really worth the extra dollars? I doubt it.
On the other hand, aluminum is more brittle than steel, and carbon fiber is much more brittle than aluminum. With a carbon fiber frame, every accident might be the last, a hard knock at the wrong place suffices to break a tube. With a steel frame, you basically need to ride full speed into a car to destroy your frame. So, this is quite a plus in robustness for steel.
In terms of durability, both aluminum and carbon have the plus that they can't rust. However, a good paint job will keep a steel frame from rusting for a very long time. My steel frame has been in heavy use for 15 years, and there's still no rust anywhere.
So, carbon gives a negligible efficiency advantage, but that's more than offset by its brittleness and high price tag. Use either steel or aluminum for commuting.