Is this the equivalent of wearing both suspenders and a belt, or something worse?

I have two pieces of window "closing" code:

1)

Code:

---

frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

---

2)

Code:

---

frame.addWindowListener(new WindowAdapter() {
                        public void windowClosing(WindowEvent e) {
                                try {
                                        socketDispatchFile.close();
                                } catch (Exception exception) {
                                }
                                System.exit(0);
                        }
                });

---

Does one obviate the other? IOW, should I get rid of the first one when using the second one?

I'm not sure which takes precedence over the other. I suppose you could write a test program to find out. But either way, I think the answer to your last question is yes.

Your code already exits so it's a waste to have the default close operation set.