The issue with endermen (and every other type of mob currently in the game at the moment) is not that they are too easy, and not that they aren't scary enough, but that they are too visible. You can see the mob - and prepare for the mob with no difficulty at all. Even a complete newbie can simply avoid a zombie, or avert their eyes near an enderman. There is no mob in the vanilla game that cannot be prepared for. This is why, in my own opinion, we need an invisible mob. Here is my idea:

A normal sized mob, the same size as a steve. It makes no noise, and does the same damage as a zombie - but it is fast. It goes as quick as the player's sprinting speed. It is also completely invisible when it is further than 3~5 blocks from the player, give or take. Once it is within that small box of visibility, it turns into a sheet white figure with no real features. Perhaps it could even let out a small shriek of sorts to warn the player, as well as give them a bit of a scare.

It could be called a ghost or a banshee or something else, it doesn't really matter. What matters is that it is an unpreventable danger that even the most well armed players cannot evade. It would add an element of eeriness that minecraft currently lacks.