XY RU Beta: Braviary was a B rank threat, while it was definitely viable, it had a hard time competing with offensive power houses such as Tornadus, Kyurem, and Azelf that were in the tier.  After a tier shift, where the aforementioned + stuff like Shaymin and Raikou moved up to UU, Braviary was a much better Pokemon, RU becomes official.  Braviary mainly stayed in RU at this point due to the buff on defog (switching into Defog boosts Braviary's Attack by two stages), Defog was not a viable move in generation 5, hence Braviary's residence in the NU tier.

XY RU:  The meta is very centralized around hazards at this point, the main form of offense is Froslass Spike Stacking HO, as such Braviary fills a very important niche in this meta game, being a defog deterrent thanks to Defiant.  Choice Scarf, Choice Band, and SpD Sub Bulk Up were all common, and all enjoyed Spike support.  It also had essentially a free switch in to the most common defogger at the time, Gligar.

Post Froslass: Froslass was placed in BL2, as it was an extremely centralizing and overpowered supportive Pokemon in the early stages of XY RU (note: they will want you to avoid calling it a "ban" for PR reasons).

Shuckle XY and Braviary's Peak: After Froslass was removed from RU, Sticky Web offense became by far the most commonly used play style in the tier.  The common formula was Shuckle + Doublade + Hitmonlee + Braviary + 2 fillers, in fact at its peak, Shuckle had over 30% usage in RU play.  This team style was so common and formulaic, and yet so very good because it was impossible for offensive teams to function against such a high powered team with reduced speed, and 2 filler slots could be used to cover any trouble spots.  It was clear that Sticky Web offense was unhealthy for the development of RU, leading to a very centralized and boring meta game, where at high levels of play, most teams shared 3-6 Pokemon.  As such, Shuckle was moved to BL2.  This was Braviary's peak, it functioned well on the common web archetype because it made defogging a bad decision and really enjoyed the boost in its speed to pick off Pokemon that were too fast to deal with it.

XY Post Shuckle: Braviary is not nearly as common or effective with the removal of Sticky Web, however it still functions extremely well with its Sub BU set, due to the fact that it very easily deals with Gligar, and gives a lot of trouble to opposing defensive teams.  Doublade's high usage makes it difficult for Braviary to ever be a truly top tier Pokemon, but it is still very threatening to the unprepared team, and a good Pokemon in the meta game.

ORAS Shift and Braviary's Decline: Huge threats fall into the tier, including several new Mega Pokemon.  Doublade moves to UU by usage, which should be a huge boon for Braviary now that its number one counter is gone, but Gligar also moves up to UU, making defog less common, and the new premier Defogger, Flygon, is much harder for Braviary to switch into.  Additionally the most common new Megas, Steelix and Glalie, really give Braviary a hard time, Steelix almost completely walls it, only worrying about CB Super Power, while Mega Glalie puts heavy pressure on it thanks to its refrigerate boosted STABs.  Overall, while Braviary is still a viable Pokemon in RU, it is pretty niche, and struggles against a lot of the most common Pokemon in the metagame (M Lix, M Glalie, Alomomola, Tyrantrum).