It means that he is a kind and caring father and that he did not have a kind and caring father when he was a child.

For clarity, I will call the man X and his own father Y. "Different from his own" is an adjective phrase that modifies "father". Thus, the sentence says that "X is different from Y". The sentence also says X is kind and caring. Since the sentence says X is different from Y, that suggests that Y was perhaps not kind and caring. However, that is only a suggestion. The sentence does not actually say that Y was not kind and caring.

His father wasn't caring but he, being a father, is very caring.

Thank you guys! I was a bit overthinking for that 🤣.

Okay, let's call this "he" Alex. "Alex is a kind and caring father, quite different from his own." This sentence implies that Alex's father was NOT kind and caring.