For many years, Roman art was considered work "borrowed" or copied from the Greeks. However, with further analysis more recently...
Roman art is a highly creative pastiche relying heavily on Greek models but also encompassing Etruscan, native Italic, and even Egyptian visual culture.
The characteristics of Roman art are "stylistic eclecticism" and "practical application." Casting in bronze became popular, adopted from the Etruscans, and the statues created were life-sized. Depicted were gods and heroes. Painting was first represented in landscapes that had been conquered by the Romans. In conquering Greece, art forms from that region spread throughout Rome. Ultimately, frescoes would become a part of Roman art.
On the other hand, Gothic art is different. First of all, it is much "newer" than Roman art. It flourished toward the end of the Middle Ages. While it appeared in the mid-1100s, it continued on into the late 15th century, and even into the 16th century in some places.
Early Gothic art was found on the walls of cathedrals and abbeys, telling pictorial stories from the Old and New Testaments, as well as saints lives. Pictures of the Virgin Mary moved away from the Byzantine "iconic" form to a woman who was portrayed with more human characteristics, including those of an affectionate and loving mother.
Secular art also found its place during this time as the world grew smaller through trade, the use of money, and a new emerging middle class. Sculpture and architecture appears before painting. There is no clear "break" from Romanesque art to the Gothic styles. Ultimately, the subjects of Gothic painting…
…became more animated in pose and facial expression...
These figures were smaller in comparison to the scenes in which they were set, and the scenes provided more "space."
The main differences seem to be that Roman art owed a great deal to the art of other countries though an influx connected to the Roman Empire's ability to "acquire" new territories. However, Gothic art spread throughout Europe, and was adopted and changed based upon the artistic patterns present in those places. In some locations, it never took hold, while in others it was accepted and evolved on its own.
Roman art reflected the culture's beliefs in Roman gods and the exploits of great heroes. Gothic art began with a concentration on the religious beliefs of the Church in Europe at a much later date.