I'll sound poetic at first though. Then I'll get to detail.
In the first three generations, early bird pokemon were the dumps in the extreme competitive tongue of pokemon players desiring no more, no less but winning and never losing a fight. Pidgeot, Fearow, and Swellow, with Unova's Unfezzant on 5th gen, were dumped by smogon to NU no thanks to their lackluster performance. Usually, a casual player who holds those pokemon dearly would give up on them once they experienced the harsh realities of Competitive battling.
Two early bird pokemon from two generations defied Smogon's and every winner greedy players. We had Staraptor who first came in OU (then Borderline as of today) who wields mighty Brave Birds, Close Combats, and Double Edges capable of busting through walls like an atomic bomb all thanks to the support of its Reckless ability. Alongside him is the newcomer, Priority Elite early bird companion named Talonflame. Raised by Usain Bolt the Thundurus, with mighty Gale Wings putting names in every enemy it strikes, Extrerme Speed found itself a new contender to compete: priority Brave Birds that puts bullet punchers to shame. +1 priority in ALL FLYING MOVES made Talonflame defy Smogon too just how staraptor Defied Smogon as well two generations ago.
Hand in hand, the wall buster Staraptor with the Lighting speed wings Talonflame join forces to rule the skies with the majestic cleric Togekiss keeping Kalos and Sinnoh out of danger from enemies alike.
Enough of the literature of awesomeness.
So, instead of repeating what all of you just said, this time, I felt like weighing my own opinions on Brave Bird vs Acrobatics.
Pros and Cons:
-A strong one shot attack with flying gem.
-Even if there's no item left after using the gem, the strength is not that impressive on the next hit
-A boosting move is somewhat a necessity to make up for the move's low power after the gem's used (mostly swords dance
Pros and Cons:
-More initial attacking power fitting for its badass animation
-the recoil syndrome is something staraptor also has (even if talonflame has the leftovers)
-with roost to keep you healed after the recoil is a double edge sword in the decision making factor: stay in or risk losing talonflame
For me, Brave bird is somewhat more rewarding despite the risks that it has in the form of recoil. Acrobatics has even higher risks in terms of having crucial KOs to consider if using swords dance.