In "that of X," the "that" is a pronoun referring to something that is owned by X. For example, you could say: "Jim's car, unlike that of his father, is a fancy, new hybrid model." Here, "that of his father" is equivalent to "his father's car."

So, "between X and Y" refers to the nouns X and Y themselves.
"One difference between Jim and his father is their choice in cars." Here we are comparing people.

In contrast, "between that of X and that of Y" refers to the possessions (or attributes) that belong to the nouns X and Y.
"I like each car, but if I had to choose between that of Jim and that of his father, I would choose the hybrid." Notice here that we are comparing cars, not people.

Rey

Ray

Thank you so much. Really helps to clarify this issue to me.

Khurram