There's a difference between Adi and Ruhi, and what they represent to Raman, other than the fact that they are their kids.
Raman was MADLY in love with Shagun. You don't forget that kind of love. And Adi was a symbol of his love with Shagun. Adi was conceived out of love and happiness. Also, Adi symbolizes a time in Raman's life where everything was perfect. He had the woman of his dreams, he presumably had a good relationship with his family and work, and he had just become a father. Adi's birth was a happy time.
Ruhi on the other hand, was not conceived out of love. She was a last-dtich attempt to save their marriage. Even her birth could not save her parent's marriage, as someone pointed out, it was the last nail in the coffin. She symbolizes the breakdown of his family, a time where everything had ceased to be perfect. In the ensuing months after her birth, he lost his wife (whom he loved more than life), lost his first born child, and the relationship with his parents had soured.
I'm not saying that Adi and Ruhi, as characters and thus people, are bad. I'm just saying, that yes they are both his children, but they symbolize different times in his life.
But it is important to note, Raman loves both Adi and Ruhi. If he didn't love Ruhi, he wouldn't have married Ishita. He wouldn't have listened to Ruhi's many demands, especially in regards to the way he treats Ishita. He loves Ruhi and is super happy to be her father. Yes he did initially take her for granted, but that's cause he had her. As the saying goes, you don't know what you have until its gone. Ruhi always reminded him of the bad time in his life. It was only after he came close to losing her, he realized how much he needed her, loved her, and wanted her with him. He loves her very much.
As for Adi. Part of the reason Raman is so crazy for Adi, is because he misses his son (obviously). He's missed many moments in Adi's life. That also brings a sort of obsession. He doesn't have the same type of visible junoon for Ruhi because she is there. But Adi is not there. And Raman is always reminded of that, which fosters his intense need for Adi.
Also, there is a certain something about Adi's birth and status as the first child. As I said before, Adi is connected to Raman's good memories of life. Obviously he will miss them. And there is a certain something about being the first child. The first child is the one that makes you a parent. The first child is the one with whom you learn as you go. The first child is the one with whom your entire life transforms. I'm not denying the importance of other children or saying that the other kids (after the oldest) don't matter. They do. Each child is a blessing and a boon. But the first child is the one who transforms you initially.
Also, we as viewers don't like seeing Raman go crazy for Adi because Adi doesn't like Raman. So we don't want Raman to be that crazy for someone who doesn't appreciate him. But just put that aside and think of it from Raman's perspective. This is his child. The child that gave him such happiness from his birth. The child who he despite loving so much, cannot see him grow.
So yeah, although I'm not a big fan of how Raman is so crazy for Adi, I can see where the obsession comes from.