Since the time the shutter opens, light hits both film and sensor at the same time, of course.

My thinking regarding Bitt's observation is that the sensor is already ON even when in darkness, before the shutter opens. It would just make no sense not to have it on and ready to accept light.When photons hit the sensor, I would agree with Bruno that the consequent electron-flow (signal) generated by the sensor itself takes place "immediatly", that is in a time which is not significant. But, are we sure? I am just guessing here.
But, I also think that chemical reaction on film is slower than sensor in anyway.
Again, just guessing. I'd be interested in finding some data.