I've run Dogs a bunch of times, and it can be great fun. A couple of comments:
(1) Dogs is a game about judgment. It works best when you play to its strengths, trying to set up hard moral choices. A young woman was semi-coerced into a marriage with a much older man who has great authority and standing in the community; she's having an affair with a likeable young man about her age. The woman and her lover are both willing to go to great lengths to continue their affair--the older man feels the need to preserve his social position and the sanctity of marriage. How do the PCs resolve the conflict? Are they willing to beat people up to force their resolution? Kill them? That's the essence of Dogs as it's written, and in my experience that's how it plays best. You can run a more traditional style of game using Dogs, where it's more about figuring out the situation or going on an adventure and fighting clear bad guys. But it's not particularly well suited to that, and it plays lots better when you stick to the hard moral choices.
2. Because it's about making hard moral choices, the best conflicts in Dogs split the PCs. Really, if I'm running a Dogs game, and the big drag out climactic conflict of the session doesn't have at least one PC on each side, I feel like I've done something wrong. (I exaggerate, in part because you really have to let the players make the calls for the PCs, but all the best conflicts I've seen have had PCs on both sides.) That makes it both a moral struggle about what the best solution is--one PC wants to break up the marriage to rearrange things so that both the young lovers are happy, another wants to drive away the male lover so that the marriage is stable and social norms are preserved--but also a struggle about how far you're willing to go. Will you throw a punch at your friend and bosom buddy to get your side of the dispute to win? Will you pull a gun? Will you take a bullet rather than back down?
3. The out-of-the-box setting is fun, interesting, and fraught with moral tensions that bite at both the characters and the players. (For people who don't know, it's a lightly fictionalized version of the early Mormon settlements in what's now Utah--so it's kinda the Wild West, but with polygamy and strong religious values.) But at the same time, it's really offputting to many players. There's a lot of institutionalized sexism in the setting, and there's an overt hostility in the setting (but not necessarily in either the author or the expected players) to homosexuality. A lot of players don't want to deal with that, especially in a serious game which orbits around morality. Being told, "hey, the socially expected thing for you to do might be to tell that uppity young woman to stick to her social role, and then to break up or punish that gay couple" can really turn many players off to the game--even when the key is "but whether you do what's socially expected or what you think is right is up to you." It does work very well in other settings, but the key is that sense of moral authority and judgment. I played in a great Star Trek: TNG Dogs game--the crew of the Enterprise was struggling over how to resolve the moral question of the week, and it ended with a great conflict with two of the PCs on one side and three on the other. It's also best if it's at least imaginable that the PCs will fight each other (hence part of the appeal of using a Jedi background story--they both have moral authority and could reasonably conclude that another Jedi who refuses to agree with them on a really major issue is turning to the Dark Side and should be fought if necessary, with the concomitant issue that a Jedi who pulls a lightsabre to enforce his or her will too readily might actually be the one on the path of the Dark Side).
4. Group composition matters a lot. I don't recommend Dogs for a group where some people just want to hack some stuff up, or go on grand adventures. And the best Dogs games raise moral issues that are unsettling and contentious for the players, not just the characters, so there's a sense that the conflicts have really grabbed everyone. That can be very hard and very rough with casual acquaintances, especially if the players have deep moral and political disagreements. You need to have buy-in, you need to have trust, and you need to have a willingness to engage. I've run Dogs at cons a couple of times, but I've mostly stopped doing that because it's not a game that I really want to play with strangers.
(Incidentally, there are some quirks in the mechanics of the system. I don't really like how d4s work (which can often represent weaknesses), and there are ways to really readily abuse the advancement system if you want to. But as long as you're playing it the way it's intended, those quirks aren't a big deal. If I were running a campaign, I'd probably talk with my players about implementing some houserules. But overall the system does what it's intended to do, produces fun and interesting gameplay, and works when used as intended. Any minor quibbles I have with it are just that: quibbles.)