I had my EA account stolen once. You know what they did? Nothing. I was able to trace the culprit's real name, his e-mail address, country of origin, and ISP via an IP address (which was not provided by EA, by the way ;-)). I did not even get a response from EA's customer service, except some drone sending me a password reset, which I did not need by then.
At least Blizzard puts some effort into it. And I can, without much trouble, get a human on the phone if I call Blizzard's customer service department.