Public executions?? How Islamic of you. Beheadings in our town squares maybe....very civilized. I'd rather watch the NBA if I need a dose of violence.
Beheading by the government is appropriate. Beheadings by terrorist groups or insurrectionists is not. One is sanctioned by God and the others are criminals to be destroyed by a legitimate government. One is done in public under government authority and the other in hiding because they know they're evil.