I've looked at it a bit tonight, since I do drive from DC-ish to Orlando-ish for a thing every year.
It looks like ticket prices vary considerably based on date, and tend to get cheaper as dates grow closer if bookings are sparse, much as airfares or hotels behave.
Depending on date, it looks like I can take one direction of that trip on a train for as low as $360. That's $75 for (what looks like decently comfortable) "coach" seating for 1, and $285 for a "standard size" vehicle.
To drive between those same two points is 811 road miles. At $0.67 per mile (the IRS reimbursement rate, which is supposed to include consumables like fuel and also less-visible things like insurance and depreciation), that's $544.
So the Auto-Train can be cheaper.
It can also be more expensive: Again, depending on date, I've seen coach seats as high as $280 -- a couple hundred bucks higher than the cheapest fare of $75 -- which makes it more rather more expensive than driving.
Trip time, if driving solo, looks close-enough to the same. It's 12-ish hours to drive straight-through, plus stops for fuel, libations and probably at least one nap of indeterminate length to combat fatigue. That seems close-enough to the auto train's ~17-hour trip to not be worth thinking too much about.
And theoretically, after getting off of the train, I won't be worn out from having spent an entire human day driving. That seems like it would be nice -- I can have a cocktail or two and play some Factorio instead of just...driving all damned day.
Fascinating stuff, I think.
I'll check out prices before I head out to make that trip again in the spring.
Who knows: Maybe I'll wind up taking the train.