Rayiner had tossed out the example of DC's Silver Line, though without bothering to state just what his argument was. I pulled Boston's BD project and ran with what numbers I could find (surprisigly scarce) to try to come up with some kind of metric for comparing total ridership capacity provided. Utility in daily trips served matters far more than cost-per-mile. And I hazily recollect that short-headway rail (DC Metro manages ... 6 minutes, by one statement, 26 trains/hr, or 2 minute headways (possibly bidirectional?) by another) does far better than a controlled-access highway.
My interest in doing unpaid, unreciprocated consulting for rayiner, esq., is rapidly diminishing, so I left off with some hazy numbers, but at least signalled that they are in fact hazy.
A USDoT source gives a maximum capacity of 2300 vph for a highway in good weather at 65mph.
https://ops.fhwa.dot.gov/publications/fhwahop13042/appd.htm
And another sorce provided a 1.55 passengers/car loading factor, US average.
The WMATA source given earlier gives 26 trains/hr, 6 cars/train (actual in service, 8 cars possible), and 120 passengers/car (162% of seated load) as maximum capacity.
Multiplication gives 18,720 passengers/hr peak throughput, a bit over 12,000 passenger vehicles, or 5.25 lanes of highway capacity. I'd counted mileage to account for the difference in project lengths: Silver == 30 miles, Big Dig less than two. Point being that the spend of the two projects delivers very different total travel utility.
WMATA's Estimated average daily ridership, all lines, 2020: 1 million. Better than the Big Dig total.
As for rail and efficiency: unlike highways, rail (through traffic coordination and limiteds) can achieve both higher throughput and shorter trip times (balanced by less frequent service to a given destination) than highways. Trip times are overall more predictable. Safety and other factors, to both users and pedestrians, tends to be better than highways also.
Further factor are that rail service (which may or may not be bundled in project costs) includes rolling stock and maintenance facilities, as well as fuel/power, and maintenance, all provided by users of highways. Rolling stock lifetimes are generally measured in decades vs. years for autos.
I don't understand what you're trying to say here. It looks like you want to draw a comparison between carrying capacity for a road and carrying capacity for a railroad. OK.
What does "the >10x advantage remains" mean? Remains after making what adjustment? The quote you provide immediately after that sentence severely undermines your implicit claim that rail is efficient by pointing out that, although the Silver Line's capacity is high, that capacity is worthless because almost all of it goes unused.
Also, you're not doing the passenger-miles-per-hour math correctly. To get maximum possible passenger-miles-per-hour, multiply 25,000 passengers by the average speed of the trains, yielding an answer in units of passenger-miles-per-hour. You multiplied 25,000 passengers by 30 miles, yielding 750,000 passenger-miles (not per-hour). (As it happens, the average speed is 33 mph, so you slightly underestimated peak capacity... except that, of course, peak capacity in reality is much, much lower, unless you'd like to force people onto the Metro.)