Difference between the usage of 'than' and 'than that'

Dear arslano,
I'm happy to help.
First of all, there's an idiom mistake. The construction "different than" is wrong 100% of the time. The correct idiom is "different from". See
https://magoosh.com/gmat/2012/gmat-prepo ... ioms-from/
I recommend our free idiom e-book:
https://magoosh.com/gmat/2013/gmat-idiom-ebook/

Let's avoid the idiom mistake by making this a regular comparative:
(a) His car is faster than mine.
(b) His car is faster than that of mine.

Here, (a) is perfectly correct, and (b), though technically correct, it too bloated and wordy to be acceptable on the GMAT.

You see, the pronoun "mine" (or "yours" or "his" or "hers" or "theirs") is a possessive that can stand in place of an understood object. Thus, "mine" is a sleek and efficient substitute for "my car".

By contrast, the word "that", as a pronoun, substitutes for any word or complete relationship in the first part of the comparison. Often, it's a very useful abbreviation. For example,
The First Symphony of Brahms is much better know than that of Beethoven.
The combined market of television and radio broadcast to cover New York baseball teams is much larger than that of midwest teams.
Do you see how "that" stands for something much longer, and so is an effect abbreviation. The problem in this sentence though:
His car is faster than that of mine.
There's really no abbreviation here. Furthermore, even if we substituted the noun in, "car of mine", that would sound stilted and awkward.
His car is faster than the car of mine.
Again, while grammatically correct, absolutely no one would say this, and it will never be acceptable on the GMAT. What's acceptable is:
His car is faster than my car.
or even better,
His car is faster than mine.

Does all this make sense?
Mike