Bioshock Infinite is a first person shooter. I have read and heard that for some that the combat mechanics are flawed in this game, that the combat itself mars the flow of the storyline, and that the game degenerates into a blood bath, where the protagonist becomes the vanquisher of hundreds of Columbian citizens and police. (cf. TotalHalibut videos on this game, which are available at YouTube) From my personal experience, the game ramps up the killing about half-way in, when one set of enemies is substituted for another set of enemies. During battles, Elizabeth can be called in to bring in assets that can aid and lengthen the player's presence on the battlefield; however, she doesn't engage in combat.
There are a few moments where the player can make a choice; however, these choices have no impact on the story.
Finally, this isn't an open world game. The player is constrained to maps that have a start point and an endpoint, with objectives constantly being updated as the player progresses through the map.