Well I am not a philologist but from my understanding, basic grammatical structures have remained the same while others have been completely discarded. But the bigest difference would be in the vocabulary since the initial meaning of many words has been changed or in many cases the ancient greek word has been replaced by modern ones coming from english,french,turkish (deriving from the 400 years ottoman occupation). So its kinda of a mixed language with let's say a 50% similarity with the ancient one. For example when I read ancient greek texts in ruins I cannot completely understand, but the main idea (wars, gods, rivarlies, knowledge etc ) is understandable.
Keep up your interesting posts!