Darwich, 35, took the top prize of 15,000 euros on Friday for a January 10 article in the French-language Cairo weekly Al-Ahram Hebdo describing police brutality against journalists during Egyptian parliamentary elections last year.
The second prize of 10,000 euros went to Lebanese journalist Habib Battah, 33, for a June 18, 2005, article in the English-language Daily Star about corruption in Lebanese elections last year.
Kassir, a prominent critic of Syria's three-decade-long military intervention in its smaller neighbour, was killed in a Beirut car bomb blast last year, one of a string of assassinations widely blamed on Damascus and its Lebanese allies.
"This prize is not just a reward, but is meant to back words against arms and barbarism," the head of the EU mission in Beirut, Patrick Renauld, said at the award ceremony which was attended by Kassir's widow, Gisele Khoury, who is herself a journalist.
Renauld hailed "the name and the life of Samir Kassir which we want to mark in the memory of the Arab world and Europe, as a symbol of the fight for freedoms".