My testing (ignoring all mission text) indicates there is no variaence to specific types of missions.
The only things that effect Fatigue are which level of mission it is (T1-1hr, T2-15min, etc.) and which level of success you got (Complete, Successful, Outstanding).
I.E.
All Tier 1 - 1 hour missions add 10% Fatigue at the default rate when you get the Successful result.