Examine the style of the two periods.
Renaissance, a term derived from the French for "rebirth," was labelled because of that exact function. The European Renaissance acted as a "rebirth" of classical styles taken from ancient Greek and Roman artists. This especially becomes explicit in the area of sculpture and fresco.
Conversely, popular Modern artists sought in many ways to directly rebel against classicism. This surge of rebellion gave birth to new types of artistic styles that branched from the traditional styles that had been in fashion since the Renaissance. For example, cubism, social realism, and abstraction were born of this era and are, stylistically, quite the opposite of classicist images.
Examine the common motivation of the artists of the two periods.
Many Renaissance artists, including Michelangelo Buonarroti, produced their masterpieces while under the direction of representatives from the Catholic Church. In fact, many artists had little say over where and what they were to produce for their patrons. They were instead valued for their technique and accuracy.
Modern artists, on the other hand, produced works in an era that has been commonly labelled as a break from the traditional patronage system. While patronage did still exist, the most popular artists, such as Marcel Duchamp and Jackson Pollock, sought to break away from what they felt to be a system of control. Unlike Renaissance artists, they had total control over what, when, and where they produced.
Examine the subject matter of the paintings.
Since the Catholic Church exercised a large amount of control over the most popular artists of the Renaissance, it is not uncommon to see that most artistic productions featured biblical figures. In addition to Christian figures, Renaissance artists also tried their hand at depicting scenes from ancient Greek and Roman texts, an appeal to their classicist roots.
What Modern artists chose to depict varies widely, from historical and mythological figures to basic shapes or complete abstraction. Subject matter in Modern art ran the gamut.