It really comes down to the driver more than the transmission:
Manual cars will generally provide better fuel economy and lower maintenance costs HOWEVER this can easily be undone by the driver.
If the driver is revving very high or accelerating often they will use more fuel with a manual transmission than with an automatic.
If the driver is bad at shifting or rides the clutch they may have to install a new clutch prematurely which is often expensive.
So, if you are an experienced driver who is looking to maximize fuel economy manual is the way to go.
If you are just learning manual or tend to have a heavy foot you may be better off with an automatic.
In terms of acceleration most automatics are more efficient then a driver with a manual transmission. But this does not mean that they are better in fuel economy.
Understand your driving habits and needs if you have the time to learn and drive properly manual transmission is the way to go in my opinion.