BC gives more health, and more AD, so for champions who don't auto attack constantly or who get large portions of their damage from abilities (Renekton, Riven, etc) those champions don't need the attack speed it gives. It also doesn't have mana, which can be wasteful on manaless champions. It's also cheaper (by over 700 gold), meaning you can get it faster as a powerspike.
BC's version of Phage is also much better, it grants you movement speed for ANY physical damage you deal, instead of just basic attacks, and it allows you to gain the +60 movement for assists rather than just for kills.
Then lastly, there's the armor shred, which massively buffs the damage you deal to an enemy, especially a tanky enemy, in an extended fight. Not only does it buff the damage you deal, but it also buffs the damage your allies deal to them, which can be a massive benefit in high AD comps, or if you have an assassin or ADC who's ahead.
As a minor point, if you've got an Ornn on your team, then BC can be upgraded to only give HP+AD, instead of the more spread out and generalist HP+MP+AD+AS+MS. You can also stack BC and it's upgrade to shred armor twice as fast, if you so choose.
Finally, if you really wanted to, you could buy both, since every single stat from both items stacks, just not the Rage passive (though you'd get the Black Cleaver's improved version).