I'm sure EB calls a lot of plays, always based off Andy's approved gameplan. Andy makes the major decisions... 4th and 1... PAT or 2 pt conv... etc because he's in charge.
I'm no guru like xen, but I bet when they gameplan an opponent, both EB and Andy collab on general strategy, 1st and foremost being the optimal way to exploit any defensive weaknesses... but also for situations like 1st and long, 2nd and short, 3rd and long etc.
Andy has the laminated situational plan which they draw up using the opponent's tendencies... and EB has the list of plays they've designed for each situation. EB selects what he thinks works best at that particular time in the game. That's likely why he and Patrick argue at times, and it's also why Patrick approached EB (not Andy) to run Wasp during the most important game in Chiefs history.
We all know "everyone has a plan... until they get punched in the mouth"... so they have to be able to adapt mid-game. Which is when Andy will sometimes override or take temporary control during a critical possession.
I don't think it's rocket science... they wouldn't be paying EB the big bucks if Andy was doing everything. Plus, coaches have egos just like players... and they want 'playing time' just as bad.
My .02