The major difference between classroom and courtroom experience is that one is real while the other is not. The information you obtain in the classroom is real, but it isn't presented in a real setting. However, when you observe a courtroom or have courtroom experience, everything you are doing and seeing is absolutely real. Although you're learning a lot of the same material, it puts it into a different light when its actually real.
Another difference is in the questions you will be able to ask. In the classroom, you have your teacher to ask about anything you'd like. You can gain as much information as you want by asking questions and listening to other students ask questions. In courtroom experience, however, you'll need to sit quietly and listen and watch the proceedings. There wont' be time for you to ask questions. You may get a chance to talk to those involved later, but it could be after you've forgotten all about what you wanted to ask.
Another difference between the courtroom and the classroom is that you'll probably get to participate a lot more in the classroom as compared with the courtroom. In class, you'll have mock trials and a chance to play all of the roles. However, until you have a degree, most of your courtroom experience will be observing or taking notes.
In your classroom, your teacher has some experience in one area of law and can teach you based on that experience. However, in the courtroom, you have a chance to be influenced by all sorts of people who have studied law and who have various levels of experience among them.