Wouldnt a turbojet engine burning hydrogen instead of petroleum be more efficient. Lockheed tested an L-1011 with hydrogen fuel decades ago.
The most successful use of hydrogen fuel in history, as far as I know, would be when used to power the Space Shuttle's three main engines.
IIRC, heavy lift rocket motors are now are being designed to burn liquid methane. But carbon atoms in the molecule gums up fuel cells.