In my opinion, one of the biggest moments that shows why The Eye picks Jon over Elias happens in Season 3. And it’s when Tim insists that he gets to help take down the circus.
Elias, who’s main goal is kickstarting the apocalypse, doesn’t want Tim to go because he see’s him as a rouge element to his plans. If he goes off the rails then it might hinder Jon’s ability to go up against The Stranger and get marked. That’s just not worth it in his opinion.
Jon however, wants Tim to go, because as he says himself, “I would rather have you were I can see you.” Jon KNOWS that Tim is spiraling. It’s very obvious to anyone around him and it’s easy to draw the conclusion that his unstable behavior is going to lead to him lashing out at some point. But, Jon is willing to risk that so he can keep his eye on Tim and see what he does when faced with the thing that took so much from him.
Jon truly and utterly serves The Eye, while Elias spends a lot of his time serving the concept of the apocalypse. What happens with Tim is a great example of that because Elias favors his plans instead of the knowledge of what Tim will do when unleashed on the circus, and that’s exactly why The Eye favors Jon as it’s pupil.