Egyptian art, especially statues, conformed to strict stylistic laws. Artists were forced to abide by rules of symmetry and were often commissioned into specific works by Pharaohs, who sought to use the works for symbolic or ceremonial purposes. Greek art was much more liberal. Varied styles were encouraged and artists experimented with different concepts of the world as they saw it. Even Greek pottery tended to have paintings and marking on it to differentiate it from others, something the Egyptians rarely did.
Egyptian figures tended to have large heads with no expression and strived for objective representation. Greek art meanwhile was much more "modern" in its embodiment of reality and human expression. Greek statues exhibited emotion, and even tissues like muscles and organs. Nudity was common in Greek art as well. While Egyptian art only used it for children and servants, Greek art used nudity profusely, seemingly out of genuine interest in the human form.
Egyptian art tended to be static. Paintings and statues were fixed in place whether portraits of people or gods, their lack of expression matching a lack of fluidity in style. Greek art on the other hand showed considerable movement. Sculptures were often designed to appear to catch Olympic athletes at the apex of a feat of physical exertion. Other art demonstrated movement as well, including paintings that captured action and interaction between subjects as if it were a mere moment in time, much like a photo.
Egyptian art was much more oriented towards religion. This is evident in a lot of the royal hieroglyphs and incantations written throughout the Great Pyramids. The Egyptians believed that their kings were divine beings from the heavens and used much of their art to honor them and assist them on their journey into the afterlife. Even the art unassociated with the pyramids and Pharaohs depicted gods and men paying tribute to the sun god Ra. The Greeks were concerned more with philosophy, and depicted thought and moral balance over religious doctrine.