Eat first. I feel it helps me improve by having the protine on board especually. I try to eat a good suzed meal about 30 minutes prior to working out.
I usually workout in the morning and i make sure to eat just when i get up then workout like an hour later just to be sure the food has been digested
I usually eat before work-out but it is not always like that. And I think that it is not important in which order you do your habits. Not all days are the same.