The more famous railroad finished in 1869 takes a more northerly route, through Ogden instead of Provo, and through Rawlins, Laramie, and Cheyenne in Wyoming instead of adjacent to I-70 through Grand Junction and Denver.
The mountainous sections of the Zephyr, specifically the crossings of the Rockies and the Sierras, are indeed the least competitive vs. driving. Based off of the official timetable [2], the Zephyr takes:
~9 hours between Chicago and Omaha vs. 7.5 hours driving
~8.5 hours between Omaha and Denver vs. 7.5 hours driving
~15 hours between Denver and Salt Lake City vs. 8 hours driving
9 hours between Salt Lake City and Reno vs. 7.5 hours driving
7.5 hours between Reno and Emeryville vs. hours 3.5 driving
Lengthening the driving time to include breaks, the train is viable between Chicago and Denver, and between Salt Lake and Reno, but is nearly twice as slow as driving on other parts of the route.
[1] https://en.wikipedia.org/wiki/Denver_and_Rio_Grande_Western_... [2] https://www.amtrak.com/content/dam/projects/dotcom/english/p...
Most of the class I railroad track was built to handle high speed (by early 20th century standards) traffic, so trains can generally reach 70-90mph (although not so much in suburban or mountainous areas) with little modification. The difficulty is that there's no economic reason to push freight trains to high speed, and mixing higher-speed passenger and low-speed freight creates scheduling conflicts, so passenger speed tends not to hit its top speeds.
[1] On freight track, that is. The NEC, which is all passenger traffic and all-electric, has higher nominal speed: even the "slow" NE regionals will hit 100mph on the empty track in MD.
[1] https://safety.fhwa.dot.gov/hsip/xings/com_roaduser/07010/se...
Also there are several sections that are particularly slow. The track through the Rockies is the original 1869 route, with original curvy single track and original tunnels. Speed there is around 20mph. Sometimes you come close to I-70, where cars are going 60-80mph. The Sierras also have slow sections. That said, those were my favorite parts of the trip.