I wake up, down a whey protein and wait 30 minutes. Then i go for my run.
Or, i wake up, down a whey protein, eat a plain potato and a banana or some berries, wait an hour and head to the gym.
I read a few studies that say lifting weights before you consume dietary fat leads to an increase in growth hormone levels, a pretty massive one actually. So i always make sure i don't eat any fats until after i workout, which is hard, so that's why i always lift first thing if possible.
I haven't read anything scientific about the benefits of running first thing, other than i know so many people that do it... that i trust to know their shit. So i've always done it myself and it helps me to get cardio out of the way. I like lifting weights, i don't really enjoy running until i am actually out there doing it.