[PaladinX]

The Brotherhood has their own tech tree completely separate from Republic Tech (If you were looking at this as an SEIV thing). They're a culture as old (Well, older really) than Terran culture, and their tech is just as advanced if not moreso.

The Hundred Houses of Hadrian were the ones who got their initial gear from the Republic, but after they captured a few major worlds with production facilities they started producing their own slightly modified Versions.

Hadrianite tech is similar to Republican tech, but Brotherhood tech is based on a completely different military paradigm, and reflects this.

The Brotherhood themselves (The Order of Exemplars) are not the sum total of their culture, they're merely the monks. The majority of their people are just laypeople. There's no government, and the Exemplars have no legal authority, but cultural tradition gives their decisions a certain weight, and the people defer to their decisions as a general rule (People tend to take the minor disputes of everyday life to the nearest Exemplar, and have him arbitrate). The point is that there is a full culture of farmers and scientists and everything in between behind the Brotherhood, so they have technology.

The third faction will have a totally different paradigm as well. They're an alien culture with very different technology.