Brave bird is Generally considered to be the better Flying type stab move for a few reasons. Firstly the added power allows staraptor to secure KOs on several important Pokemon.
Ex.
1 32 Atk Staraptor Dual Wingbeat (2 hits) vs. 9 HP / 22 Def Sylveon: 122-146 (68.1 - 81.5%) -- guaranteed 2HKO
+1 32 Atk Staraptor Brave Bird vs. 9 HP / 22 Def Sylveon: 183-216 (102.2 - 120.6%) -- guaranteed OHKO
Without Brave bird you would not be able to secure the Ko on Sylveon greatly diminishing your sweeping potential.
Dual wingbeat also has the issue of missing and while missing is uncommon consistency is almost always preferred in VGC especially on a Pokemon like Staraptor who is functioning as your main damage dealer a lot of the time. The recoil from Brave bird is also not that bad because you can typically just heal it off with a Pokemon like Sinitcha and even if you can’t its much more important to not take a hit from something like Sylveon compared to taking a bit of recoil.
Source: Ive used a Staraptor team for most of Reg M-B