If you had to pick one word to describe the difference between Romanesque and Gothic architechture, it would be "light". Romanesque is characterized by it's name-- "Roman-like". Most notably taken from the Romans is the round arch. The principle feature of the arch is the ability to distribute top-down weight onto focused columns, opening up the central areas of buildings greatly. This distribution of vertical weight naturally led to buildings reaching new heights and new levels of openness. The Romanesque period is sometime classified as dark and cramped but it is an unfair comparison made in light of the succeeding Gothic era which took the concept of height and space to new levels.
If you could make any critique of the Romanesque era it is that their characteristic arches and groin and barrel vaults are, from a pure engineering perspective, objectively less sophisticated than the architechture of the Gothic era. The round arch distributes weight to its supporting beams quite well save for the very center, which bears the weight of the material above it. This limits the load that any given Romanesque armature, a building's skeletal frame, to a given height and or thinness. The innovation that French architects borrowed from arches first seen in Persian Sasanian architecture, passed to Islamic Spain was the pointed arch. This key innovation did two majors things:
In a traditional Romanesque rib vault, four semicircular arches coming together to form a box would result in a transverse arch that is larger than the side (arcade) arches. However, the point arch affords an incredible amount of flexibility in allowing the arcade arches to be the same height as even the transverse arches, permitting vault compartments of endless different shapes and sizes. The semicircle made popular by the Romans proved to be limiting. Gothic vaults came to form intricate webs in the ceiling, every architect after the other pushing the boundaries of "how high can we go with how little". In my opinion, Gothic architecture is squarely in my book under the label of "terrifying".
The pointed arches distribute the weight traditionally and perilously placed on a equivalent round arches keystone and divides it between the two, channeling even more of the top-down weight onto it's two arms. Less weight from the top means, of course, that Gothic architects push the envelope. Again, Gothic architects, armed with a keen understanding of physics and engineering and perhaps fortunately lacking a normal man's understanding of gravity, choose to take a major stability innovation as an excuse to go higher, thinner, grander.
With popularity of stained glass windows essentially replacing walls, and the soaring open space vaults that carry the eye towards heaven, Gothic architecture becomes entirely synoymous with "light". And this was th goal. God and heaven was keenly associated with the concepts of light and height, and Gothic architecture, wrongly seen a few centuries later in my opinion as a distortion of Classical architecture, was more of an cultural imagination of the glories of paradise. Gothic architecture served as a reminder to the faithful of both the beauty of heaven and their alien distance from God's graces. Abbot Suger of the Saint-Denis cathedral, wildly considered to be the birthplace of Gothic architecture, described his innovative church as if he were "dwelling... In some strange region of the universe which neither exists entirely in the slime of the earth nor entirely in the purity of heaven." He called the colored light of his own little piece of paradise "Lux Nova".