"He waited for the moment when he felt it was right. He wanted to do it for years really. I think it’s out of envy and anger. But I don't think it was something that he particularly enjoyed doing it. He didn't want to talk anymore because he knew Juan could change his mind. It was hard for Cesare to kill his brother." ― François Arnaud.

It's so bittersweet that Juan was the only one who felt Cesare's constant pain, and he was glad he found something to relate to with his brother, with a relieved smile. He found solace in the fact that he could empathize with him as he endured pain all the time as well, albeit for different reasons. I wonder if he ever knew whether Cesare's suffering stemmed from being trapped in a cardinal's robe and not having a career as a soldier. Also, you can see the frustration and conflict on Cesare's face, as if he doesn't want to kill his brother but he has to since Juan became a liability and would eventually bring the family down with him, especially after Juan's descent into addiction, illness, and madness. Cesare is driven by the desire to preserve the family and because he wanted Juan's undeserved position as a Gonfaloniere. All in all, these two tormented brothers were trapped in their father's vicious cycle of favoritism and ambitions, which caused the tragic ending of their brotherhood when they could have been brothers in arms.