The one on the left is rather more worn than the one on the right, and looks to have been replaced several times as well (it doesn't have any rivets on it). This is a pattern I've noticed with other sets of double doors on campus, too.
I wonder if the left door is favoured because we drive on the left in the UK, or if it's a more general phenomenon. If it were to do with handedness, I'd have expected the right door to be the one that was opened more frequently. Maybe it is, but people put their right hands in different places?
Personally, I tend to kick them open so I don't have to get my hands out of my pockets.