I have no liking for such a man as he.

and

I am not as great as he is.

is the second sentence correct? if yes, why there is a difference between between the two sentences? if no, why? and what could be the corrected sentence?

A pronoun is a word used instead of a noun.The second sentence is the correct form of a sentence.Here 'he' is used as a personal pronoun which denotes the person been spoken of. 

The first sentence means: I do not like people like him.

The second sentence means: He is greater than me. 

Both the sentences are correct.