The Romanesque architecture represents massiveness, while the Gothic is more represented by verticality. You will also see semi-circular arches in the Romanesque, versus the pointed arch of the Gothic. Due to gaining more mathematics knowledge, Gothic architecture had prominent features such as rib vaults and larger apertures that allowed more light than the smaller Romanesque apertures. Gothic cathedrals also had more detailed and intricate westwards generally speaking. Quintessentially Gothic is the flying buttress, while we mostly see standard Buttresses in the Romanesque. One thing you will see in both Romanesque and Gothic architecture is the Latin cross layout of cathedrals.