He currently plays a pretty conservative style, he doesn't rush the puck much and seldom roves in the offensive zone. I think a lot of this is due to playing with Chara. If McAvoy guesses wrong or is caught down low its almost an automatic breakaway for the other team because of Chara's lack of foot speed.
That said, there are a few deficiencies in McAvoy's offensive game. He almost never shoots the puck from the point. He'll defer to Chara, or he'll look to a teammate to pass. That part of his game is frustrating to watch. For those who remember Tomas Kaberle, McAvoy's reluctance to shoot is very reminiscent. When McAvoy does shoot, its usually not a very good shot. He doesn't have a strong or accurate slapshot.
If he starts taking more risks offensively I can see him being a 50 point defenseman, but I don't see him regularly getting more than 10 goals a season.