Pick one.
can no longer just grab 
and choose later depending on the game. Your runes, masteries, build path, playstyle, etc. entirely depend on this choice now, and it comes down to whether the new BC is worth losing Brut in the build path. So which Riven are you?
Drunk Rummate6 votesAlways ghostblade. Cleaver build path sucks for Riven. Low AD, no pen, rage passive is completely unnecessary with her kit, and she's supposed to kill squishies in 3 hits so she won't benefit from the shred unless she's 1v1ing a tank... in which case LW is still better.
Hard4Hamsters4 votesGhostblade is better until the target has 150+ armor, which you should be targeting squishies as Riven anyway.
Dreadlocks2 votessimple... Ghost blade vs squish Black Cleaver vs tank. nothings changed. /Thread.
ScreamPaste2 votesGhostblade is better in almost every scenario for Riven, the active makes up for the rage passive, and makes her a better split pusher, as well as making her harder to kite.
I'd only take Cleaver against a tanknificent/CC heavy team, while forgoing my CDR runes.
Kingsgrave1 votesWhy not both?
ScreamPaste4 votesBecause Riven doesn't have time to apply the armour shred in team fights, benefits more from ghostblade's active than the rage passive, and cleaver's build path sucks for her.
You're better off buying LW with that money.
junglerboy163 votesbasically, have your tank jungler or support pick up BC for you and you're set.
SleepyLionCub1 votesJust get both. A hydra. A bloodthirster. Cdr boots, and a warmogs.
ScreamPaste7 votesAnd do what with 50+% CDR? I won't even start on the random warmogs.
AMYS GRAVE1 votesWhy not both? Ghostblade first though...
Wînter Fox5 votesBoth is a waste. Everything Riven has scales with AD, you don't want to gimp her by stacking a bunch of low AD items.
RaptorKarr1 votesI'd go BC because Ghost Blade just isn't as good as it used to be on Riven, not to mention Riven doesn't even Crit anyway or even need Crit, the Attack speed is good I guess but the HP from BC can keep you alive longer even if it's just a little longer, if your looking for Attack speed, nothing is wrong if you take Zerker boots is there?
The Sword Saint1 votesBC vs a tanky team where you're gonna be in a lot of sustained fights, GB vs a squishy team you can jump on and burst down.
Mr Broken Wings1 votesDepends completly on the enemy toplaner / enemy picks for me. Against gnar for example black cleavers movementspeedbuff is enough to outrun his jump, its godlike against him. Overall ghostblade/early tiamat riven is snowball heavier and has an earlier powerspike, if you can use it then youll go for that build, otherwise black cleaver.