The settings in both stories are very important. Without "Greasy Lake" being set where it was (at the trash-filled lake at night), the story would not have the same effect. Also, had "Battle Royal" not been set in the "Deep South" during a tumultuous time for African-Americans, it, too, would not have the same effect on the reader.
There are also symbols in both stories. The lake represents a baptism for the narrator in "Greasy Lake." Once he enters the lake and runs into the dead body, he experiences an epiphany about what his life has become. Things aren't as fun as he thought they were. The blindfold in "Battle Royal" represents blindness on the part of both the protagonist and society. The protagonist is blind to the world around him (Caucasian world) and society is blind to the plight of the African-American population, in many ways.
The tones of both stories are similar, actually. There is an uneasiness in both stories, an unsettling feeling. The reader can anticipate that something bad will happen in both stories.