The Egyptian and Greek ways of death were very different. The Egyptians were very into the afterlife and the soul continuing to live, whereas the Greeks were very interested in the burial of the body, having a very nice funeral or ceremony, and having an important grave stone. Also, the Greeks believed that the afterlife was a very bad place in the underworld protected by Hedes.
The Egyptians made a very big deal out of the death. They would take the body and mummify it by wrapping it many garments of cloth and then put it in a tomb. The organs were put in jars because thats where the soul was and it would rise to the afterlife where it was tested. The God Horus would weigh your soul against a feather and if it was lighter, it could move on to the afterlife where they would happily move on http://www.sacred-texts.com/egy/ebod/).
The Greeks would have a huge ceremony for a death. The funerals were very extravagant and they made nice gravestones. They believed that the afterlife was a bad thing because they would go to the underworld with Hedes. People would rather stay and live a poor unhappy life then go to the underworld.http://www.metmuseum.org/toah/hd/dbag/hd_dbag.htm