Both have their benefits and downsides. I know that's a lame, cliche'd response, but seriously, it still applies here. COR is better in almost every conceivable way, except that they lack Haste.
Though just doing some quick mental math, Samurai roll (With a SAM in the party) increases a SAM/DRK/WAR/DRG's WS frequency by at least 20% which is almost a 20% increase in overall damage. Polearm SAM can go from 5-hit to 4-hit which is almost a 25% increase in overall damage.
I know, in most circumstances, you'll have Haste and Haste gear which will cause Marchx2's usefulness to rise exponentially, but regardless, COR is only using one roll to increase WS frequency by 20%, and the other roll can be Corsair's Roll, for a 15-20% increase to exp gained. Now all of a sudden COR gives that 35-40% increase while all BRD gives is 20% Haste from both songs combined. (Even though in most situations, that double March is closer to a 33-40% increase anyway...)
My point is, just because you don't look like you're visually attacking faster, doesn't mean you're not doing more damage or getting better exp overall. Ideally, you'd have both jobs in your party, yes. But if you don't have the option, the two jobs are interchangeable provided the COR doesn't mind pulling.
Edit: People will always have their bias. Mytoy is COR, so obviously he prefers COR. Ninian is BRD so obviously she prefers BRD.
Edit2: in really top-tier merit parties, a BRD would be pulling with Mamoolbane, Trollbane, Lamiabane to eliminate the time wasted waiting for the Colibri to cast Elegy. It's not fair to argue that BRD has Elegy, therefore it's better.