While both are ok, I would say that 'operate' has come to imply a more physical interaction - using your hands to make something function in a certain way. Thus, one might operate a machine.
'Run' is more often used to imply a less physical involvement. For this context, 'run' and 'manage' are more likely to be considered synonymous than 'run' and 'operate', given common usage.
I say again, a dictionary will tell you that both of these sentences are fine and I agree that you could choose either. I recommend using 'run' based solely on common usage.
Hope that helps.