Turbo engines are inherently more fuel efficient for a number of reasons, the main ones being:
- smaller displacement means less friction for a given engine output rating
- less throttling at part-load reducing pumping losses
- exhaust waste heat recovered by the turbine can return some energy to the crankshaft as intake pumping work
The reason mass-market downsized engines return poor full-load efficiency, is manufacturers have to add excess fuel to suppress detonation and thermal stress. Actually they don't HAVE to - water injection would do a better job and save a lot of fuel.
Furthermore, the fuel economy standards set around the world tend not to include full load testing. Result? Vehicles with impressive advertised fuel economy and abysmal real-world economy - especially if the vehicle has to work hard.