Maybe the right question is not "What architectural styles prevail in the New Eden factions?" but "What do the inhabitants of New Eden's factions need from their architecture?"
Proper worldbuilding in a setting where more or less normal human beings populate the vast majority of the universe's habitable spaces should start from the ground up. What do the people on [Planet A] need from their surroundings to feel safe, comfortable, and fulfilled? The answers to that question will help build a picture of how said people would build their homes and cities under ideal conditions.
Next, of all possible resources (physical materials, technical knowledge, and wealth), what do the people of [Planet A] have to work with when building? The answers to that question will help us understand how said people would reconcile their ideals and dreams with the realities of their world in the creation of a plausible settlement/colony/city.
Of course, we do have a few examples from PF of how certain things have been built. Dam-Torsad, for example, or the Crystal Boulevard in Caille stand out in my mind. In those cases, we have the final product and can analyze it to trace backward to answers that will help illustrate the qualities and character of the people who live(d) there. Perhaps, however, using major central municipalities and capitals like Dam-Torsad is misguided as the prevailing realities of life in much of the Amarr Empire, for instance, is almost certainly very different from that which prevails on the homeworld. If nothing else, of course, the PF on architecture that does exists can provide insight on broader cultural currents if not necessarily details on what the average dormitory looks like on a colony in Anohel or Agoze or wherever.
Reconciling this view with the reality of the game world, I think only in cases where pre-fabricated structures or pre-programmed and standardized construction technologies are feasible and economical will there be much widespread copying of architecture. In at least one case in New Eden this is both feasible and economical--starship and space station design.