A quick answer that grew into a dissertation...
Easton carbon bars are tested to withstand 10 times the load of their comparable aluminum bar. Be it flat to flat, riser to riser, DH to DH. Each and every bar is tested at a level that would snap its aluminum counterpart prior to being boxed up and shipped. I do not know what any of the other manufacturers do, so I can only speak as to Easton. No I don't work for Easton (as if that is a good thing). Carbon has strengths and weaknesses when compared to both aluminum and Ti. The big thing with carbon is to watch for over clamping in the stem, break lever, shifter (as if), bar ends. The second thing to watch is for gouges, or any other thing that could be a stress riser. Aluminum has nearly the same issues. Both aluminum and carbon are more prone to failure when stress risers are introduced. That is why they shot peen (mat textured look) aluminum, so that any stress areas are relieved. Aluminum can take direct impacts a little better than carbon when it comes to scratches or light abrasions. That is why they have to overbuild carbon cranks, so that there is limited weight reduction over a comparable aluminum crank. Without too much background: 6000 series aluminum is less effected by scratches and dings than 7000. 7000 is stronger per weight than 6000. My aluminum bar preference would be 6061 over 7075. Neither carbon nor aluminum give much warning prior to failure. Since carbon is somewhat still a "black art"for some companies, I would stick with one made from the big boys. Otherwise, I don't feel it is worth the risk. Then again, I would stay away from cheap aluminum too. Easton, Answer, Raceface, and Titec have all served me well. I have seen both break, and in both cases it was just at the interface with the stem. The aluminum bar was a Trek specked item. It happened on a jump. One side snapped, the other bulged as if just prior to a snap. The rider seperated his shoulder. The carbon bar was an early riser. I think maybe an LP, though it has been a while. It happened in a g-out, and not a major one. The rider cracked (did not fracture) his collarbone. After that, I rode exclusively Ti up until finally succumbing to the comfort of a riser. Ti does not usually critically fail like aluminum or carbon. It usually bends, and does not spring back when at its limit. Right now I ride an Easton Carbon XC low rise. Even with their testing, I don't feel comfortable using the SL for extended intervals. If I went back to a strait bar, and could affort it, I would be happy with the Titec 118. Then again, I have broken both collarbones in several places. Call me a wuss I guess.
General rule of thumb:
-Ti-nearly unlimited fatigue life, bends instead of snapping, replace if it bends or develops a crease. Oh and protect the ends as it is so thin. My 118 is now 23.5" wide from trimming the ends a few times.
-Carbon-nearly unlimited fatigue life, snaps at failure, don't buy used or suspect items, replace if gouged or any sign of delamination.
-Aluminum-about 1/10th the fatigue life of the two above, will bend slightly then snap at failure, don't buy used, replace about each two years or after a major hit.
Oh and finally...the oversized bars should be better than a traditional one in terms of strength at this critical junction. Having said that, they are likely stiff as hell. Something to keep in mind if you are running fully rigid.