a. Man's intelligence is greater than animals'.
b. Hawks' vision is better than humans'.
c. Hawks' vision is better than the other animals'.
Can one use the above sentences or does one have to use 'that of' instead of the apostrophe?
The vision of hawks is better than...
'that of' cannot replace the apostrophe. You could say that 'the vision of hawks is better than that of humans'.
So, both b and c are grammatically OK
For a caution is required: the intelligence of man is..... and, the intelligence of men is...
in the first 'man' refers to all men as a group and may not be true in all circumstances whereas 'men is' gives a more general impression.