Neither the “engine”/“power generator” distinction you are attempting to make, not the statement “gas burns at a higher energy than steam”, is physically meaningful. It is true that supercritical steam turbines operate at a lower temperature than gas turbines, and if the cold reservoir of the Carnot engines in question were at the same temperature, that would indeed make gas turbines potentially more efficient. But in fact gas turbine outlet temperatures are much higher. This is why adding a steam engine to the output of a gas turbine makes it more efficient. (This is called a “combined cycle power plant”.)

The actually relevant distinction is that gas turbines, like other internal combustion engines, have a much higher ramp rate than external-combustion engines like a steam turbine. This makes “peaker” gas turbines a crucial resource for establishing power grid stability.