We had a long discussion about this point one time while trying to kill time in Korea. The AF does in fact receive extra pay at some locations, but it is not hardship duty pay though commonly called HDP. HDP comes in 3 flavors. HDP-L (Location) is based on your specific location and is in increments of $50 up to $150. The locations are determined by DOD and the same for all services. HDP-M (Mission) is based on the job you are assigned to. This is mostly the Joint groups that search for and identify POW/MIA personnel in Laos, Cambodia, North Korea, Vietnam etc. HDP-I (Involuntary Extension) is for personnel involuntarily extended in a location. Mostly it happens in Iraq/Afghanistan. More information and the location/amt for all HDP can be found here.
http://comptroller.defense.gov/fmr/07a/07a_17.pdf
As it was explained to me, the reason the AF sometimes gets extra pay is because the gov't quarters on a certain base may not provide the AF minimum amount of living space. All three services have different standards. For example, consider an O-1 staying in unaccompanied transient housing (like you would be assigned to for a school). The AF requires a minimum of 460 sq ft. The Navy requires 250 sq ft and the
Army requires 90 sq ft (sorry XMSR3). If an AF personnel is staying on a Navy base that only provides 250 sq ft, that person would receive partial BAH (Basic Allowance for Housing) to make up the difference in minimum standards.
I found the most current housing standards that I could for each service. If you are bored and care to read them here they are.
http://www.afcee.af.mil/shared/media/document/AFD-070919-082.pdf
http://www.apd.army.mil/pdffiles/r420_1.pdf
https://www.housing.navy.mil/navfacpubs/Eligibility_for_Housing.pdf
I'm not an expert in this area, so if any other priors see something wrong please point it out.