In the books he comes off almost tyrannical since it's often from the POV of Tyrion that we see his actions. Tyrion killing Tywin was almost cathartic as a book reader.

However, as a show watcher it's a different story. We were given those scenes between him and Arya, his hard-assed approach with Cersei, Jaime AND Joffrey, along with myriad other scenes fleshing out his character (like with Tommen). Despite his ice cold demeanor, he's an incredibly compelling character to watch because his motives are understandable.

Just look at the reactions in the other thread on the deleted scene between him and Pycelle. People don't necessarily "root" for him, but it's clear they enjoy his scenes.

I'm telling you, there's gonna be eulogies in Tywin's name once he's gone.