The limits for wings are pretty straightforward, given that you're trying for some degree of realism. Anything human-sized, with the mass of a human plus however much the wings add, is pushing the limits of flight. I won't call it impossible to fly, not when even larger pterosaurs have done it, but wings big enough to allow more than gliding for a humanoid are going to be very long: I would guess 5 metres at minimum for wingspan (tip to tip), possibly more.
Before I dive into this breakdown of flight and its hazards, I should warn you that it may be overwhelming. Not every story needs this degree of analysis, and of those not many need to actually display that analysis to the reader.
This is with the intent of helping you set rules to define what your fliers can or cannot do, which is helpful for self-consistency (basically, not contradicting yourself). Those rules don't have to be limiting your creativity, though: this sort of analysis gives you lots of sources for dramatic tension by exploiting the resulting strengths and weaknesses and can often provide inspiration.
The Mundane World
The musculature needed to power those monster wings is going to have to be similarly monstrous. These fliers are going to have massive chests simply to accommodate the huge muscles they're going to need to flap those wings: the flight muscles take up around 20% of body mass in most flying animals. I don't know where the assorted organs are going to get pushed around to by that problem, but note that the lungs and heart are also going to have to grow to about double the typical human size to keep up with the demands of that musculature. Reader's questions regarding the resulting appearance are up to you to deal with, but if nothing else these guys will need to eat accordingly. Assuming they are otherwise largely human apart from the wings, they're all going to be chomping down on food like champion weightlifters if they're using those wings at all.
You also need to keep the local temperature in mind. Open wings expose lots of surface area to the air. In tropical or desert regions, this does wonderful things for keeping you from overheating. In a colder climate, however (picture pretty much anywhere that can reliably expect to receive at least some snow each winter), this is a liability, because you're at risk of freezing to death very rapidly. Eating more for extra energy to produce more heat will help (I'm assuming your humanoids remain warm-blooded), but there's a limit to how much that can do for you in the face of that ridiculous amount of surface area. Clothing isn't going to be a viable solution: even if you could do it for those wings (I'd like to see someone try it!), the bulk and weight is probably going to cripple the ability to actually, you know, fly. There's a reason all the larger birds and bats of the modern world are native to the tropics. Your protagonist is going to want to stay far away from places like Canada or Russia, and trapping them there could be very effective for their enemies (see: dramatic potential).
It's worth noting that physical exertion in itself is not necessarily a problem: if the body can appropriately support the strain of powered flight (basically, you need an oversized heart and lungs to supply the necessary oxygen to the flight muscles, as noted above), this has the side effect of rendering you pretty much immune to fatigue. Barring severe thirst or starvation, you'd be able to fly for hours as long as the sky was cooperative, or run a marathon without too much trouble, so endurance will actually be very impressive in most cases.
Given the size of these flying humanoids, you will be bounded when it comes to taking off under your own strength, and convenient cliff sides or balconies probably won't be that common. The force needed to make that crucial leap into the air, at that weight, simply cannot be supplied aerobically (via oxygen), and anaerobic muscle contractions come at a price that mean you are incapable of lifting off too often. I'm running off this very useful source for details: it's based on pterosaurs, but the relevant principles here don't change that much between pterosaurs and the largest birds (which face the same problem).
Essentially, you've got about 60 to 90 seconds to get into the air and find a good source of lift (most likely a thermal or a suitable wind pattern) before the muscles falter and require some rest. This is entirely feasible at the speed you'll be moving (covered in detail in the next section) since you can cover some distance to reach the spot in question, as long as there aren't obstacles in the way. Still, it means that if you get ambushed and try to fly out of the area, you will be limited in how much distance you can open up in that first burst; if you can't find cover within a range of about two kilometres (yes, you're really going that fast), you could run into problems if you're forced to circle around a thermal while you recover. Also, if it's cold (nighttime, during winter, etc.), you're going to have a harder time staying aloft.
The large wings introduce another problem: maneuverability is going to be limited, especially with bird-like wings. You've already noticed that this is a problem in tight confines; the wingspan alone means you need plenty of space around you in the air to avoid crashing into anything. The main roads in your typical downtown would probably be flyable, but trying the alleyways would be for the daredevils, as it would border on suicidal. As for tight turns, I can't necessarily rule those out entirely, since folding one wing in could plausibly make a quick spin, but you'd need room to fall before opening your wings again, so flying too close to the ground could be a problem.
It's also important to understand that staying airborne requires speed; given the sizes we're dealing with here, you're going to need a lot of it, which can be good or bad depending on the situation. Based on the source I linked, you're soaring almost as fast as somebody driving on the highway (think 70 to 80 kilometres per hour as a rough minimum, because you're quite possibly exceeding 100, and definitely will be if you exert yourself). On the one hand, pursuers are going to have a hard time catching up if you're on the move, since you won't be limited by those silly things called roads. On the other hand, lift is provided mostly by how much air is moving under the wings, which is largely determined by airspeed (outside of hovering, which is impossible for biological wings to manage at anything near human size). There are ways to adjust your angle of attack or your wing shape to move the limits around, but essentially there's a minimum speed for you to stay aloft, and it's pretty high in your case. Even if your wings could support tight turns, you're going fast enough that trying that is likely to splatter you over the face of something.
You mention gunfights, which lends me the impression that these guys might be trying to fire guns from the air. That is a Very Bad Idea for a few reasons, but the biggest one is accuracy. Even the horse archers of the Mongols and so on saw their accuracy plunge when firing on the move, and they were on more or less level ground; trying to aim for a single attacker who is likely behind cover while you're moving in three dimensions at once is an excellent way to waste ammunition while the other guy takes the time to line up a nice easy shot on the giant target that you've made yourself into. There's also recoil: in the air, you don't have anything to brace yourself against, so the first shot you take is going to spoil your aim pretty badly for a few seconds, which means any sort of rapid-fire weapon is idiocy (you'd probably be limited to handguns in terms of practical firearms, which don't tend to fare well compared to rifles in a firefight). In short, they would probably stay on the ground in any sort of shootout.
Also, think back to that huge wingspan. Five metres or more, and wings require a lot of surface area to function. That's one giant target for anybody with a ranged weapon, especially at close range; you describe the wings as being bird-like, with feathers, but anything like a net or a spreading weapon (think video-game-shotgun, not standard rifle) is going to do horrible damage. Lots of things for you to think about before you open your wings anywhere near your enemies.
Reality sometimes offers all the answers you need. You don't have to invent any sort of societal constraints or obviously contrived situations to keep these wings from being overpowered: working (more or less) within the confines of realism offers plenty of ways to do that just with physics and biology.
It's worth noting that wings, in nature, are evolved arms: I'm aware of how many sources of fiction like to have flying humans with wings coming out their backs, but evolution says that's creating two extra limbs from nowhere (in other words, thoroughly absurd). Most such stories do rather require their flying humans to have usable hands, though, so it's usually necessary to overlook this fine point for the sake of a good story. I suppose my point here is that perfect obedience to realism and science is less important than internal consistency in a story: if you need to bend something, then bend it. Just make very sure you don't bend it the other way later, because that would be very sloppy writing.