Assuming you are doing roundtrip, so there is also the drive back from Herndon to Union Station on Thursday (?). In that case, I would definitely do air from EWR to IAD.

The Sunday drive is unpredictable. It probably won't be too bad, but it can be. Also, you'd be using the regular lanes on the toll road, not the Dulles access lanes.

Also, you get the miles... This is assuming that the airfare is reasonable. I'm guessing it should be ok, as it is the DCA market that can be crazy prices, exploiting the fact that there are many business travelers.