Do we get to compete as an alliance against others or is it pve?

Wow, a simple question with complex answers. Simple answer is yes. The whole storyline of the game has you find out that the center of the state you are in has a building in the center that is basically the capital. This capital is taken only by an alliance, and winning it gives certain bonuses.

Beyond that, there are a massive list of events that pop up every week, and some have you score points as an alliance to compete against others. There are zombie laor scoring ones and plenty of other competitions they are working to release.