Sum up:
Spider-man Web of Shadows is like Spider-man 2 & 3 before it; with a huge open and explorable overworld in the form of New York. Like Spider-man 3, you can switch between Spidey's black symbiote suit, which is more powerful, and allows him to hit harder and lift larger objects; and the classic red suit, which allows him to hit and dodge faster. The customizable skill/power system is back, and this time Spidey can finally swim in water. However, the most mentionable addition to this game is the inclusion of a moral system, where your choices will change the overall story (and eventually the ending).

Recommended age:
The ESRB rated this game "T" for Teen, listing "Animated Blood," "Drug Reference," "Mild Language," "Mild Suggestive Themes," and "Violence." The "Animated Blood" probably consists of the symbiote enemies' (which the story revolves around) gooey black consistency, and there's likely no red-colored blood present in this game. The "Drug Reference" might refer to some sort of serum or scientific formula, and there may be some light references toward some of the drug dealers you might fight.

The "Mild Language" probably consists of d*mn, hell, a**, and slang like "suck." The "Mild suggestive themes" must refer to some of the screenshots/videos that depict the Blackcat kissing the (somewhat) reluctant Spider-man, and she and a few other female characters wear some moderately revealing/form-fitting outfits with a very decent amount of cleavage shown.

And last of all, the "Violence", which of course, consists of Spidey kicking and punching enemies, and there's most definitely some mass explosions, people being kicked through walls, etc. So overall, if you've let your thirteen year-old play the previous Spider-man games, then this game isn't any more extreme content-wise. I'd recommend it for ages 13+.