The actual brochure for the 2008 WRX indicates that you get better gas mileage with the 4spd:
Fuel economy (city/highway) Manual: 19/24 mpg
Automatic: 20/25 mpg
And that the driving is adaptive so if you are doing a little spirited driving (called racing in my day ha ha) then the automatic will presumably shift at higher revs.
4-SPEED AUTOMATIC TRANSMISSION
Balance performance and convenience with the
direct control of the smooth-shifting SPORTSHIFT
automatic. Around town, driver-adaptive programming
maximizes fuel economy. In more spirited
driving, the transmission automatically delivers
more enthusiastic shifting response.
Here is a link to the brochure in case people are interested.