Both? Neither? I guess it depends on what kind of productivity we're talking about. My body and mind are not in sync right now.
I am absolutely not an early bird. Baby Brother has me waking up early on my days off because I have to puke, and then eat breakfast, before 8. If I have chores to do on Saturdays, I usually do them in mornings, as long as they don't require thought. The brain doesn't function in the a.m., but my body is ready to work. I can be productive with physical things like running errands and cleaning.
I'm not really a night owl, either. These days, my body is tired of moving by about 8, and I can't seem to do any housework after that, nor can I muster the energy to actually leave home and go somewhere. Nate goes to bed at 7:30, and that's a good excuse to make sure we're home by 7, which is my current preferred curfew. Usually, I spend my evenings on the loveseat. If I have things to do that require thought, such as blogging, designing materials for Full Life, or reading something I need to think about and want to remember, I get started on it around 9. My body is tired but my mind is active. I am most productive with creative things at night.