This Monastic church clearly shows what defines Romanesque differently from Gothic Architecture. St Alban's was originally founded to commemorate the 3rd-century Roman who would not turn in a Christian. So Alban paid for it with his life on this spot. (Bede tells the story in his History.)

Originally a Romanesque church (with rounded, Roman arches for support), St Alban's was added to many times. When Gothic became the rage in the thirteenth century, the church was extended (it has one of the longest naves in England) and Gothic Arches and windows were added.
 
Inside St Alban's, one important development is apparent: the earlier, rounded arches on the right are Romanesque, the pointed arches on the left (a later addition) are Gothic. The advantage of the Gothic Arch, beyond its aesthetic qualities, is that it can support much more weight than the rounded arch.  

This difference is mirrored in calligraphy: early medieval uncial letters were rounded, while the later Gothic script (late 12th century and following) is very pointed and more angular.  

In terms of structure, the round, Roman arches tend to support the weight on the top. Sometimes the weight literally flattens the top of the arch -- a case of "fallen arches"! The pointed arch does not support the weight at the top, but the point forces the stresses down and out, most of the weight going to the pillars which are much more able to stand straight under a great deal of strain.  

For more on the Gothic-Romanesque difference, see Le Mont St-Michel. For an improvisation on the Gothic arch, the Bodleian Library, Oxford, has a good example of "fan vaulting".  

To illustrate how far twelfth-century technology had progressed from previous centuries, see these Anglo-Saxon structures. (Photos by M. Markowski) 
It is important to bear in mind that the very word "Gothic" was a term of derision. It refers to Goths, the Germanic barbarians which destroyed Classical Culture.  Renaissance scholars saw the only previous, real "Life-of-the-Mind" in the Classical Age. From the perspective of the Renaissance, Medieval was the age between  Renaissance and Classical -- the "Middle" Ages -- which brought true culture down into the gutter, or further, into the abyss of darkness, superstition and chaos.

That view of Medieval/Gothic held sway until 19th-Century Romantic thinkers rejected the cold, "objective" rationalism of the Enlightenment and looked anew for inspiration in the Medieval Age. Currently, the debate continues without abate: The word "Medievalism" still conjures up the lack of humanism, or stated in another way, the presence of inhumane ways of being, acting and becoming. What does the evidence -- on both sides -- suggest to you as a solution to this inquiry?