Far as I can tell, there's different rewards for each side. When ranking up commendation categories, Diplomacy is included, but they want you to focus on using the Duty Officer system.
Of course, since the unique reward officers are the same regardless of which category you max out and Diplomacy has outside sources of commendation points, what I've been doing is leveling up in star clusters by doing diplomatic missions only and trying to do as many duty officer assignments as possible so that I'm putting the system through its paces and, at the same time, getting extra points and side-stepping the inadequacies of flying a Lt. Commander ship at Captain.
Then, I'm going to make a Klingon and level him up exclusively using duty officers.