It's can be a little frustrating for a response to essentially say "it depends", but that's the case here. There are three main types of automatic gearbox used by car makers today, with dual clutch (DCT) and continuously variable transmissions (CVT) and more conventional torque converter 'boxes going toe-to-toe with manuals. Each has its own advantages and disadvantages, and while a manual gearbox might produce a fractionally better official fuel economy figure than an automatic, autos have become more and more sophisticated over the years so the difference has become increasingly negligible. How you drive has a far greater impact on economy than what gearbox your car has, and real-world driving is somewhat different than the processes involved in official testing, so while the on-paper figures might slightly favour manual cars, you may find it easier to get closer to those official numbers in a car with an automatic gearbox, simply because there are fewer variables involved (EG at what revs you change gear, which gear you select on hills, and so on). Maybe we should have just left it at "it depends"...