It used to be that manual transmissions were the hands down winner for better fuel economy. However this is no longer the case. Modern automatic transmissions are more and more efficient. Todays automatic transmissions can even provide better gas mileage than a manual version.
There is no clear cut winner. Depending on the make/model of vehicle its possible that either the automatic or the manual transmission could provide the better gas mileage.
Here's just a couple examples. I looked up the cars in question on the government Fueleconomy.gov website. Below are screen captures of the results. First the Chevy Sonic is one car where the manual transmission has better efficiency.
On the other hand for the Honda Civic the automatic transmission is better.
You can no longer assume that a manual transmission will provide better mileage. It really depends on the vehicle in question.