I am going to advance a theory about The Brave One that I readily admit seems hard to stomach.
What I think makes The Brave One brilliant is that, while it's perfectly acceptable as a mediocre vigilante thriller, it's also utterly superb as a commentary on vigilante justice, via commentary on mediocre vigilante thrillers, by virtue of accepting its status as a mediocre vigilante thriller.
The thing about vigilantes is, of course, that their existence is predicated on the narrative power of their actions. While his whole schtick is empowering the individual to become the centre of his own universe and all that, the paradox of the vigilante is that he relies completely on his presence in a larger diegetic whole in order to make sense of his role.
The just plain old hero can walk into a situation and save/defeat/befriend as he sees fit. Though it's a slightly outdated way to look at the hero (nowadays heroes can't do heroic without a dark, mature chapter in which yadda yadda yadda, the upshot of which being that almost no hero created in the last twenty-odd years is without a pinch of antihero to his character makeup), the traditional concept of the hero is one in which the entire universe, for our purposes, pretty much revolves around our guy.
Whereas the vigilante, without a larger context, is just a crazy guy. No vigilante story can run its course without at some point establishing that the Law can't take care of the problem/the Lefty justice system just coddles murderers and degenerates/people don't know what's right no more/etc. This bigger world continues to push and be pushed by the vigilante as he goes about takin' care of business: it's very rare that you'll see a vigilante tale that doesn't include the chapter where we see what the Man On The Street thinks of our guy, whether it's via newspaper headlines or a background talkback show (this is a good device because it situates the vigilante in a world of dangerously unhinged people while reminding us that yes, but he's the right kind of dangerously unhinged) or just what other characters are saying about the vigilante when he's out of earshot. (Alan Moore has often said he was disgusted to see his uber-vigilante, Rorschach, adopted as some sort of hero-figure by people who just glossed over the parts where his contemporaries complained that he stank and was totally lacking in the social graces; Both Batman and Spiderman, a couple of the c20th's most enduring vigilantes, occupy universes in which every other fucking person is a plucky journalist determined to get to the bottom of this whole beating-up-criminals thing).
So being that the vigilante is completely reliant on being part of a larger narrative that forces him to go about his grim business, and being that once he does so, a huge part of the story is what uninvolved third parties think of said business, the vigilante myth becomes as big a part of any given vigilante story as the vigilante himself or any of his leering, cowardly victims. And so the smartest vigilante stories - The Dark Knight Returns or Memento, for instance - become hugely meta affairs in which the story interrogates the myth scrutinises the character.
The script for The Brave One is not one of the smartest vigilante stories. The script for The Brave One is actually kind of shit. The cops banter like movie cops - "Rap sheet as long as my dick!" "No priors, then?" - and the attempts at poetry feel strained and inappropriate (beyond the acceptable, ie this is not just a story about a woman who talks a lot but is not very poetic) and there's a weighty subplot that feels yanked from a whole nother movie, one which would have a hard time getting cinema release.
And yet there's something about the depth of Foster's performance - making all the standard phases of the vigilante's-progress story feel less like waypoints on a well-travelled timeline and more like believable human behaviour - and Jordan's compassionate yet interrogative storytelling that forces you to give it more credit than that. This is a consistently gripping, impeccably well-told story that hits all the standard beats, but provides a counter-rhythm in which the whole business-as-usual vigilante fable is quietly second-guessed every step of the way.
And ooohh, but am I on the shakiest of shaky ground here, because if you liked The Brave One, you'd be inclined to see the cloying idealisation of Foster and Andrews' relationship as clever deference to the obvious trope where obviously the demise of the most perfect relationship ever is what sets the whole murderous rampage in motion; whereas if you weren't so hot on The Brave One, you'd be liable to say, well, they just never had that much chemistry to begin with. And if you liked The Brave One, the horrible business with all the gun-swapping and story-setting at the end would just be a piece of business to be breezed through before the somewhat lovely ending; whereas if you didn't like The Brave One, if it never managed to get you on its wavelength, that would be the ending, and damn if it wouldn't break the whole fucking movie for you.
Which I suppose means that your warmth toward The Brave One may depend on just how addicted you personally are to the modern myth of the loose cannon who takes matters into his (slash her) own hands; which I suppose, it being now and all, makes The Brave One something of a classic bit of communal dreaming.
 My way of solving the perpetually-thorny gender-assignation-in-brief-references thing here will be to adopt the convention of The Brave One and always refer to the vigilante as male until we're specifically talking about Jodie Foster's character.