Literary techniques are used by authors and poets for emphasis and in order to create images in the reader's mind which help to develop situations or characters. To Kill A Mockingbird is full of literary references beginning with the title of the novel itself which is highly symbolic and relates to the prejudice that surrounds an innocent Tom Robinson and his trial for raping Mayella Ewell. The mockingbird represents all that is innocent and significantly it relates to the quote in the question- "Your father is no better than the n*****s and the trash he works for" - because it speaks to the intolerance of society and the tendency to pass judgment without any justification especially considering the supposed victim is the town's own definition of "trash." Accordingly, there is much irony in Mrs Dubose's comment from chapter 11. Irony is a literary device and in this story it develops the theme as prejudice defines the people of Maycomb County.
Prior to Mrs Dubose's comment, the reader learns that Scout and Jem hate her because she is disapproving of everything they do and suggests that they will amount to "nothing" but Atticus insists that they are courteous to her. However, on this particular Saturday, Jem responds to Mrs Dubose in a tone that she considers disrespectful. Although Jem tries to ignore her rudeness, her comments are intended to incite him. She appears to have no idea of her own faults.
The quote is ironic because the community of Maycomb County would rather support the Ewells. They live next to the rubbish dump and are considered white "trash" by the locals and yet the community ignores their own prejudice against the social standing of the Ewells as being less offensive to them than an honest Tom simply because of his skin color. Therefore this quote is also a play on words because it has a double meaning. It reflects Mrs Dubose's own obtuse sentiments and reveals that she supports her own version of "trash" in her intolerance.
Personification is another literary device which has been used in referring to the "trash" in this quote because trash is given human characteristics as if a person can work for it.
First, a comparison is being made between two things. There are lots of ways to make comparisons in literature. Probably the easiest to recognize, and a common comparison tool, is the simile. It is a comparison between two things using the words "like" or "as." For example, "He is as nasty as a hungry tiger." Your quote is not a simile. It lacks "like" or "as."
Other comparison techniques that do not use "like" or "as" include metaphor, analogy, and allegory. Allegories use symbols to represent abstract ideas. George Orwell's Animal Farm is a good example of an allegory. Your quote doesn't fit this either.
Metaphor and analogy are very closely related. They both are used to compare two unlike things. "She is the black sheep of the family" is a good metaphor. Obviously the girl is not a real sheep. The sentence simply illustrates that she doesn't fit in. An analogy will do the same thing, but is typically a more robust explanation of why two dissimilar things are similar. "A cell is similar to a car, because . . ." would be an analogy. It's more like a logical argument.
Your quote is closest to a metaphor, because it doesn't use like or as to compare Atticus to his clients. It would be a simile IF "no better than" were replaced with "like."
Additionally, the sentence uses the word "better." That's a comparative word (as opposed to a superlative). Comparative words compare and judge two things. Superlatives do three or more. Consider better vs. best for example. Or worse vs worst. The statement isn't saying Atticus is the worst, just no better.
The quote makes use of colloquial vocabulary that is reflective of the time period and place. Notice the word "nigger" is used instead of "black" or "African American."