To me, classical critics focused more on analyzing poetic elements and adherence to classical structure.  Romantic critics, on the other hand, had the sentiments of Romanticism in mind.  They would focus more on the emotional impact of the piece. I should note that the enotes study guide is very thorough here.  You will get more out of that then we can write here in these short posts.  You can read it here:

http://www.enotes.com/criticism-from-plato-eliot-salem/criticism-from-plato-eliot