Train: Auto-Train costs $280 per head, flat, for minimal accommodations. (Transporting the car itself is... free? I guess?)
Driving: The IRS mileage rate is $0.67 per mile (which is supposed to cover fuel and other easy-to-spot consumables, as well as purchase price and insurance and depreciation and and and), and the distance is 811 road miles between those same two points that the Auto-Train covers, or about $527.
Based on these assumptions,
For one person, the train looks cheaper. It is $280 to take the train, vs $527 to drive.
For 2 people, it's very close the same price: It is $280 per head to take the train, vs $264 per head to drive.
For 3 people, driving pretty clearly takes the financial win: It is $280 per head to take the train, vs $176 per head to drive.
The background noise should be much less than a plane, and the air pressure etc is obviously normal, but the erratic noise can be more -- e.g. some clunks if the train stops.
That IRS rate is incredibly high. It's probably around $150 or so in fuel depending on prices and efficiency to make that trip. I can't see food, insurance, and depreciation adding another $300. The ability to not drive is what can make it worthwhile for some, as you note.
I am skeptical about the ease of scaling this, especially given the state of non-car distance travel on Amtrak.