First, let’s note and set aside the "on purpose" redundant structure, which is often used as a way to put emphasis on something, like in :

Je choisis David. ("neutral" expression)

C’est David que je choisis. (emphasis on the object)

C’est moi qui choisis David. (emphasis on the subject)

Regarding the meaning nuance, very litterally, « Ce que ça fait » (personal experience / subjective and perceptive) is indeed not the same as « Ce que c’est » (universal nature / objective and definitional).

1. mais il ne sait pas ce que c’est que de vivre sur une île isolée:

As a native speaker I would literaly translate that to "but he doesn’t know what it is to live on an isolated Island".

2. mais il ne sait pas ce que ça fait de vivre sur une île isolée:

Literally this could be translated as "but he doesn’t know how it feels to live on an isolated island".

As you correctly guessed, both sentences serve to express a sense of frustration at the ignorance of the person referred to as ‘he’.

However, in sentence 1. you could easily drop the second ‘que’; it would still be valid French (as far as my experience goes) and doesn’t change the meaning.

The first ‘que’ in that sentence is grammatically necessary; you wouldn’t be able to write or say "*mais il ne sait pas ce c’est que de vivre sur une île isolée".