Do You Remember Lucid Dreams As Well As You Remember Regula

For those who can lucid dream, after you wake up is your memory of the dream more, the same, or less detailed than your memories of regular dreams? And does it matter whether the lucid dream was early in the night vs. right before you woke up in the morning? Right now I don't remember my normal dreams very well. I'm working on that with a dream journal. I'm curious to know if this means that even my lucid dreams will be fuzzed out as much as my normal dreams are.