What will be the better approach for sending data from an Applet to a JSP page for processing, using "appletContext and showDocument()" or "setting up an URL Connection and passing data through a stream"?
This depends on what your applet is trying to accomplish. Calling showDocument() could affect the frame the applet is running under, which would shutdown the applet, and even if the same applet was created on the resulting HTML page, this would restart the applet.
If your applet is only a form and is expected to shutdown, then showDocument might work. If you are targeting results to alternate frames in the browser window, showDocument(url, frame) could also be useful. Note that any data passed via a showDocument call necessarily would be sending data only through a query string.