It's not about a "dark and gritty" angle, but rather a groundlevel approach that, even when fantastical, offers perfectly logical explanations for everything. The Avengers moved away from this with their douchebag redshirt aliens, but stuff like Amazing Spider-Man embraces it.
Batman Begins features a man whose methods may be "supernatural" but where does he get his power? He's been the head of an international terrorist operation that's existed since the dawn of time. They're not just evil, they've seeded themselves within the corporations, institutions, everyday ways of life that we see in cops, politicians, etc. Also, his satellite partners utilize a toxin which may as well be magical, but we see exactly HOW Bruce bloodies himself finding in the roughest terrain finding a precious flower that can produce these results.
Of course, Nolan can get away with this because he doesn't have a binary concept of "good and evil." He also can't resist showing Bruce flipping through circulars in building his weapons (which turn him, in a way, magical - no one just vanishes from a room in mid-conversation). So it's a very specific point of view.
That HAS been adapted in future superhero films, but because there's a less nuanced take on good and evil, we're treated to smaller universes, more casual plot conveniences, more ground-level details. Amazing Spider-Man is probably the guiltiest of this, showing him meticulously building his webshooters, piggybacking off the science of his parents, wooing the daughter of the person in the city who misunderstands him the most. It's charming sometimes, like the one moment where Spidey exasperatingly texts and calls Gwen Stacy in mid-Lizard brawl (less charming on paper), but other times it's simply more of a serious-faced approach that feels the need to explain and over-explain the fantastic. It's not so much grim-and-gritty as over-detailed-and-mundane. You know, so people can relate to it better (i.e. you know, for kids).
Of course it's still early, but there's reason to believe the new Superman does similar things with another fairly uncomplicated view of good guys and bad guys, and a desire to make Superman more "relateable." I very much hope I am wrong.
