love how both tywin and ned are genre definingly different from the predecessors from their houses. lannisters have always been the clever house, from lann the clever swindling casterly rock to tyland lannister splitting kings landing's treasury. but tywin's 'low cunning' and use of brutal crushing military force to solve his problems which he employs in the reyne-tarbeck rebellion and the scouring of the riverlands and the red wedding is different from the historical version of house lannister. it's a new brand of lannisterism, tywin's version, and it is this version of lannister legacy that he passes on to his children.
ned on the other hand very much likes to distance himself from the stark features of the wild and the wolf's blood, which other starks like brandon and rickard and cregan and even lyanna are defined by, adopting instead an ethos of duty and honor more like the tully words or his foster father jon arryn. he does this because he thinks that it is this wolf's blood that killed them in the end. just like the lannister kids contend with their father's idea of a good lannister, the starklings contend with their father's idea of a good stark.