You can use either one. Because JApplet actually extends Applet, much of the functionality is identical. There are a few differences, however.
With JApplet, you have access to the content pane, which can be called using getContentPane(). If you have a content pane of your own (such as a panel) that you want to replace it with, you can call setContentPane(). When you add components to your applet, you add them to the content pane, not the frame.