"Harrison Bergeron" is told in third person limited point of view. This means that the story is narrated by an outside figure, not a character in the story, who is able to know the thoughts of one character in the story, George Bergeron. Events, however, are related objectively.
The point of view of "Hills Like White Elephants" is third person objective. This means that no thoughts of the characters can be understood, only speculated about. This is significant because it is clear that the characters are in the midst of making an important decision (whether or not to have an abortion), and the word abortion is never actually mentioned. It leaves the audience to make inferences about the thoughts of the characters.
I have linked to another question answered about point of view in "A Rose for Emily", but will summarize that response here. "A Rose for Emily" is told in first person point of view from the point of view of a townsperson in Emily's town. This is significant because the townsperson cannot see things the way Emily sees them, but can only make inferences about how or why she does the things she does.