The only difference is that the computer-delivered test uses a keyboard and the paper-based test uses a pencil. All other aspects of the IELTS test are the same such as the content, scoring, level of difficulty, and question types in the Listening, Reading, and Writing sections.
In the computer delivered LISTENING test, the timings are slightly different from the paper-based test as the paper-based test requires 10 minutes time to transfer answers to an answer sheet. However this step becomes redundant when answering directly on a computer. Therefore, in a paper-based test, Listening is for 30minutes + 10 minutes; however in computer based it is only for 30 minutes.