I've been playing Vayne a lot, and I'm having trouble deciding whether Cleanse or Quicksilver Sash is more efficient.
I'm not sure it's a good idea to compare them - while they do the same thing, they have very different costs.
I'd say only go Cleanse if there's dangerous CC in bot lane, and you might need the summoner spell to avoid losing early game, which Vayne is usually bad at. Otherwise, use that slot for Heal (or maybe Exhaust), again mostly for early game. Basically, you spend this summoner spell to keep you alive before you have time to farm up and get items.
Quicksilver Sash on the other hand, is a mid-late game item buy. You get this to survive in teamfights when the enemy has CC that can lock you down. Most team comps have at least some CC, and if you're playing Vayne correctly, you are probably their #1 target, so you should expect to eat all of those abilities. The question isn't really "should I get Quicksilver Sash?" but "when should I get Quicksilver Sash?". You want at least one big item (i.e. Bloodthirster, maybe Phantom Dancer) to really boost your damage, and then think about your next items. If there's a lot of enemy CC, you might pick up the Quicksilver Sash next; if you think you can survive the teamfights, you might instead buy another big damage item, and only get the Sash if the game goes long.
If they have Malzahar/Urgot/Warwick and focus you, you should go for an early Quicksilver Sash (probably after Infinity Edge/Bloodthirster or after Infinity Edge/Bloodthirster + Zeal).
If they just have a team with a lot of stuns/taunts, it's a good idea to run Cleanse instead and go full damage with your build, and get a Guardian Angel later.