Depends on the competition. If I had to put over a hundred arrows consistently in the spot at known yardage, I would go with aluminum. Like JimPic says, carbon doesn't have the consistency in spine or weight to do that job consistently. I've had carbons try to swap ends in a strong crosswind. So, no matter the competition format, if it were an extremely windy day I'd go with a heavier aluminum arrow because they are less affected by wind than carbons.
You constantly hear the old song 'carbon is more durable than aluminum.' When comparing aluminum and carbon shafts of similar weight, then yes. Thin walled shafts are amazingly fragile. But go with a shaft that has a wall thickness of .015" or more and an outside diameter of 22/64" or more, and durability becomes a non-issue. I'd put my old favorite 2216's and 2315's up against carbon any day in a durability test.
For sure, those big ol' fence posts are heavier and don't fly as fast. Big deal! I never shoot at game beyond 30 yards anyway. Within that distance, speed and flat trajectory benefits of carbon are miniscule at best. And the heavier arrow absorbs more energy from the bow, leaving less to be turned into noise, or that has to be absorbed by expensive string suppressors, vibration dampers and such. Of course, if you use all that vibration damping technology in association with hefty aluminums...
Aluminum arrows have been getting the job done since Doug Easton finally began marketing them in 1939. He had several world archery champions shooting them in the years prior to that. They are perfected, and have been perfected for many years now. Carbons are still having growing pains. They're slowly getting better but are nowhere even close to being on a par yet with aluminums for consistency.
Aluminum is only dead for those who don't know any better.