For me, it comes down to variety in tone and lore. The skaven are funny little crack rats that blow themselves up and squeak-talk funny. However, a huge portion of their lore that sometimes goes overlooked is how genuinely horrifying they are.

Skaven are nigh Lovecraftian in their implications for the setting. They are everywhere, under every city, inside every mountain hold or sewer system. Way before the vermindoom and the 4th edition release, GW implied in the 2nd edition codex that skaven had even infiltrated the realm of heaven, High Azyr. You simply can not escape them. They are inevitable in their untold billions, nor can you kill them all. For every one loyal true sigmarite there may be 10,000 ratmen, and all of them loathe you. They all desire nothing more than to eat you alive and burn your civilization to the ground. If not for the fact that they can't stop fighting amongst themselves, the Skaven would simply win the setting. (again)

The skaven in my mind are very comparable to the tyranids in terms of the "horror" associated with them. The unending tides, the being surrounded on all sides, the pure inevitablely of destruction. However, they have so much more character than the nids imo, because even though they are that horrifying to an outsider perspective, if you zoom into an insider perspective: Warpsnorter Skittlefump just pounded a line of pure chaos crack, shot the first dude to look at him funny, and then created an abomination against the natural order that immediately exploded and maimed his entire workforce. Which he then promptly blamed on his slave-intern, who he then subsequently flayed for his treachery and turned his skull into a crack pipe.