The TriStar would have had limited use for any length of time - at the end of a long spares supply line and incapable of replacing the C-130.
Whereas a (properly equipped) Atlas can do all the in-theatre fixed-wing South Atlantic tasks, replacing both C-130 and Voyager. It can also use both RWs routinely (unlike the TriStar) - and fit in the Timmy hangar (unlike the Voyager). No doubt it could also be 'missionised' for coastal maritime surveillance as well.