This is one of my favorite shooters out right now, and I love playing it. From about 10 hours of playing the campaign and multiplayer, I've noticed some things.
I will admit, the game earns its M rating because of the campaign, because I'm telling you, the language is insane in the campaign. The soldiers swear everywhere, from mission briefings, to full scale battles. The violence isn't so bad, your typical shoot the bad guys violence, nothing to serious. So if your child is younger, don't let them play the campaign. It's gretty, and isn't even that good.
The multiplayer is what really makes this game violent. The games new engine, frostbite 3, allows almost the entire environment to be destructible . You can flood cities and destroy your environment to gain a tactical advantage. You can't do that in call of duty. The battles require a strategy and communication with your team. Your team will need to work together in order to win. There is hardly any language in the multiplayer, but soldiers do occasionally swear when they are about to be blown to bits by a grenade, but its hard to understand what they're saying. The violence isn't so bad, it's the same shoot the bad guy stuff, and again, you can destroy buildings. That's awesome.
So hopefully this long review helped you decide if this game is appropriate for your kid. It's really up to you.