I would define "human brain capacity" differently than "human brain's capacity".
It's partly emphasis — the former emphasizes human , while the latter puts the stress on brain —; but it's also that brain capacity is a quantity, while brain's capacity is a capability.
Thus, it makes sense to talk about The human brain's capacity to do something , but not really about The human brain capacity to do something .
english.stackexchange.com/users/1547/Marthaª
The human brain's capacity to do something is amazing.
The capacity belongs to the brain, so we use the possessive form, which is brain's .
Note that the two examples you give are sentence fragments, since they do not have a finite verb.
english.stackexchange.com/users/100/waiwai933
You can say this several ways.
The capacity of the human brain — in other words, human brain capacity — is something to behold.
A human's brain capacity is something to behold.
The human brain's capacity for knowledge and adaptation is seemingly limitless.
All are correct.
english.stackexchange.com/users/2303/Robusto
To enlarge on Martha's answer, I think the quality/quantity distinction is the key to the answer, when you realise that "capacity" as a quality always belongs to somebody or something - "my capacity to ...", "the government's capacity ... ", "the capacity of the average citizen to ... ".
The quantity does not need to belong to something grammatically, (even though it will actually be the capacity of something): "The capacity is 400ml" is fine, whereas "The capacity to eat" is odd (not impossible; but the possessor of the capacity must have been established first).
Hence "the human brain's capacity" is possessed, and therefore can mean the quality or the quantity, whereas "human brain capacity" is not explicitly possessed
- it is just a kind of capacity - and so can usually mean only the quantity.
english.stackexchange.com/users/547/Colin Fine
The human brain's capacity is 600 billion neurons.
english.stackexchange.com/users/None/
What is the correct version please?    The human brain capacity to do something.  The human brain's capacity to do something.
"human brain capacity" or "human brain's capacity"
english.stackexchange.com
<grammaticality><possessives>
english.stackexchange.com/questions/6535
english.stackexchange.com/users/2711/Francisc
It is generally agreed that the correct term is "human brain's capacity". The capacity belongs to the brain, so we use the possessive form, which is brain's. Some people think there is a difference in the wording and that the first definition emphasises the human where the later emphasises the brain. Some people think the sentence simply means the brain's great ability, that is why the possesive form is used.
It is generally agreed that the correct term is "human brain's capacity". The capacity belongs to the brain, so we use the possessive form, which is brain's. Different meanings. 'Brain capacity' is quantity and 'brain's capacity' is capability
It makes sense to talk about  the human brain's capacity to do something, but not really about  the human brain capacity to do something . The capacity belongs to the brain, so we use the possessive form, which is  brain's .    In this context "human brain's capacity" makes more sense than "human brain capacity".
I would define "human brain capacity" differently than "human brain's capacity" stresses the ability of the brain.
I would define "human brain capacity" differently than "human brain's capacity" stresses the ability of the brain.
There is difference between them. "Human brain capacity" emphasises the human, whereas "human's brain capacity" It means the great ability of the brain to do things.
 I would define "human brain capacity" differently than "human brain's capacity".  It's partly emphasis — the former emphasizes  human , while the latter puts the stress on  brain  —; but it's also that  brain capacity  is a quantity, while  brain's capacity  is a capability.    Thus, it makes sense to talk about  The human brain's capacity to do something , but not really about  The human brain capacity to do something .
In this context "human brain's capacity" makes more sense than "human brain capacity".