Cleanse vs. Quicksilver Sash
Solution 1:
Cleanse removes:
Cleanse is a 'non-targeted' summoner spell. It is mainly used to remove crowd control effects to escape or catch a target. It cannot be used while suppressed but can remove most disabling debuffs. Unlike Quicksilver Sash it reduces new debuffs after all current ones have been removed, making it a more effective escape mechanism.
However, cleanse cannot be used to remove suppression effects:
Cleanse cannot be used while suppresed, and thus can not remove spells like Warwick's Infinite Duress, Malzahar's Nether Grasp and Skarner's Impale.
Quicksilver sash (QSS) removes almost any debuff but does not have the same duration reduction afterwards that cleanse benefits from. QSS is a great buy when you are a target of suppression ultimates.
Solution 2:
QSS gets rid of supression. Cleanse doesn't. :) The MR is also fantastic. Use your judgement, depending on the enemy.
Solution 3:
Quicksilver sash can remove any detrimental effect including Mord's Ultimate and ignite as well as all CC, but Cleanse can only remove a limited number of CC
Solution 4:
The have some similar uses and some different uses.
Cleanse DOES remove ignite, HOWEVER cleanse does not remove suppression. Suppression abilities, Malz's ult, Urgot ult and Warwick ult can ONLY be removed with QSS. Note that you cannot remove Mordekaiser ult with cleanse, only QSS can.
Cleanse is really most useful in removing hard CC's like Galio ult, Sona ult, Amumu ult and a wide variety of hard stuns that people use to lock down AD carries.
QSS removes everything, plain and simple. Great counterbuy as an AD carry.
Solution 5:
It mainly depends if you are worried about early game cc and ganks. If you champ has little escape and is easily ganked cleanse will give you the needs to get away, but I find people use it so they don't have to spend the gold to get quicksilver because it tends to more of a late game item.
Champions like Yi who are targeted very fast late game get it sometimes to prevent too much cc on him. Quicksilver is used late game and cleanse offers early game protection. Also quicksilver gives MR.
Champions like Kass or Mundo get it to prevent too much focus early game, while say Master Yi gets it to prevent too much cc on him while he eats up the enemy team
TL:DR? Cleanse is early, quicksilver is for late game and you are too power so you are targeted too much.