I think the better question is: How awake are you when you experience it? Dream reality and waking reality are pretty close to the same in terms of our sensory perception which is the only way we can judge "what is real?" Our brains take in the sensory data and "project" reality onto our internal screens. We are able to do this in dreams without any sensory data inputs, but if we simply sleep through them, we never really experience the level of "reality" that dreams have. This is why we want to have lucid dreams so that we can be awake when we are experiencing dream reality. Then we can make the evaluation of how real it is while it's happening, instead of trying to experience it from memory.
Have you ever had a dream, Neo, that you were so sure was real? What if you were unable to wake from that dream? How would you know the difference between the dream world and the real world? Morpheus