That intuitively makes sense - obviously a big vehicle needs more energy than a small one like a car.
However, typical city bus routes spend most of their time under 30 mph, cutting aerodynamic drag by a whopping 90% compared to 70 mph highway cruising that a car does.
With more work on rolling resistance (buying super-good bearings and fancy tyre designs), regen round trip efficiency, and energy use of the passenger cabin (heat pump heating, double glazing), I could see busses needing similar size batteries to electric cars and still being able to do a full days city work.
In turn, that makes the energy source fairly irrelevant from both an economic and a social perspective.