Romanticism and Classicism exist on two very different poles within literary movements. Many new periods came about as a reaction to the previous period, and the contrasts between these periods are no different.
First, to differentiate between the two, we will begin with their differences in how they regarded nature. The Romantics believed that nature was powerful and constantly changing. The Romantics believed that nature was a force that would/could never be fully understood. Unlike the Romantics, the Classicists believed that nature could be rationalized and, therefore, completely understood.
Second was the differentiating thoughts on truth. The Romantics believed that one would only find truth through their own intuition given they highlighted the importance of individual thought and not societal thought. The Classicists, instead, believed that truth existed only as a result of reason. They found that imaginative thought failed to be able to be studied scientifically and, therefore, upheld no realistic function.
Third, ties into scientific thought differences. The Classicists believed that man should conform to universal thought and ideas. The Romantics believed that they should embrace their own individual innovations. Perhaps the most poignant quote to exemplify Romantic thought on tradition and innovation is from William Blake:
I must create a system or be enslaved by another mans; I will not reason and compare.
Basically, the Romantics believed in the endless possibilities which man could change the world, and they embraced them. The Classicists, instead, held up the importance of adhering to what has already been said and done and mastering only those ideals.