You're right that the Rams have the advantage for the next 3 years. The only thing the Rams have to worry about is that they make him angry and he walks after that. I don't think they have to worry that he will sluff off in his play. If it's not the Rams in 3 years, he has to keep his level of play high to get that huge contract with another team.
AD has to worry that the Rams will string him out the next 3 years. A significant injury during that time means less to the Rams than it does to AD. This does force him to consider taking a bit less than the market may value him at, just to have that guaranteed money over the long haul.
So the Rams do hold the cards, but in 3 years, AD could walk.
NewMexicoRam