This is one of those questions that seems like a no-brainer -- a bunch of people are sharing a ride, so they must be saving energy. When asked this question, we all think of a full bus or train of people vs. the number of cars that would have carried the same people.
The key issue turns out to be occupancy -- how full is the train or bus. And it turns out that occupancy is probably lower than most people think. That is because everyone rides on buses or trains as they commute -- they are going in the direction of most people's travel at the time of day they travel, so the transit is totally full. But no one thinks about those trains having to go back the other direction, usually mostly empty. As a result, we get to this fact, from the National Transit Database as synthesized by Randal O'Toole.
2014 Energy Use per Passenger Mile
- Transit: 3141 BTU
- Driving: 3144 BTU
Valley Metro Rail here in Phoenix does better, at a reported 1885 BTU per passenger mile. As reported many times here on this site, the cost of building this rail line, now well over one and a half billion dollars, would easily have bought every round trip rider a new Prius, with a lot of money left over. This would have saved more energy as well. Buses in Phoenix are averaging just over 6000 BTU per passenger mile.