Well, WRT fatigue. When you set your setting to Fairly Fresh, it means players come as soon as they can after you get to Fairly Fresh .. meaning almost all their minutes are at Fresh. When you set them at Getting Tired, it means they will come out asap after they hit Getting Tired .. meaning that the 'Extra' minutes they play is at 'Fairly Fresh'.
As to efficiency, I am not 100 percent sure. But, as the computer wants to put the starters in at the end of the game (if it is close), and at the last 2 minutes it sometimes lets them get slightly more tired that you set, it stands to reason that the starters (having played more minutes in the 38 to that point) can be a bit less fresh at crunch time.
For the record, SIM AI usually plays at Getting Tired .. and I sometimes play my best players there as well .. but if I press on Defense, I normally do Fairly Fresh.