For a lot of people, being 'productive' to them means burning the midnight oil which is hardly actually productive. If you do things when you are alert it makes them more effective. It also gives you the rest of the day to just breath and not be hard on yourself for getting tired and your performance faltering throughout the day; after all you got all that stuff done earlier. Ever have a weekend when you got everything you needed to do done by noon? The day becomes yours and you feel like a superhuman.
for me it depends on what I'm doing. if its something creative then i find I get better results late at night. if its more technical then early in the morning.
the quote from hemmingway "write drunk, edit sober" comes to mind, if you replace drunk with tired