Well this is a more difficult question than we might think, an assassin in popular terms is usually someone agile and subtle, someone who must be more flexible than fast.
Leather would be the most obvious choice but in terms of its use it is not really the most adaptable material to the situation, it protects even more than fabric but at the same time it becomes hard over time.
Just think about it, you are an assassin who spends days outside a city waiting for your target to move or position himself in the perfect place to finish him off. In that time the leather can get hard, limiting the wearer's flexibility and in turn worsening the effectiveness of their missions.
Now if we go for example to the cloth, the cloth is an element which is essentially silent and essentially versatile, but for a murderer who can be surrounded and has no form of defense, it leaves him more vulnerable, but compensating much more for its flexibility and speed.
The point here is that depending on the situation, leather is much better, because although the same armor can harden over time, it can always be soaked in hot water and restore its elasticity.
Of course this in the case of being a colloquial murderer which we are used to.
Then there's the other class of serial killers, who don't care about their armor or gear and are going straight to kill you with an axe, so those could just as easily go naked with a spear and stab you in the eye.
If this were D&D it would be a Mix between Barbarian and Rouge , a character who will kill directly without being subtle because he likes to kill .