Both show a passion to push things to their extremes. Aemond strives to become the greatest ruler in the history of Westeros through studying and training, and Chara’s entire character revolves around the idea of of control and limit-pushing through their association with the number 9.

Also, both have strong connections to their mothers. Aemond very clearly vies for Alicent's approval as stated by Ewan, and Chara’s manner of speech is nigh identical to Toriel.