I typically play the medium level of a game to assess balance. The "medium" level is typically one where the human and AI play on a level playing field.
Certainly "hard" difficulty can make the game more challenging, but this has never been too appealing to me, because this is typically done by arbitrary bonuses and penalties -- giving the AI production, economic, tech, military, or other unearned advantages, while penalizing the human player. Such arbitrary advantages and penalties are a poor substitute for a competent AI that can provide a reasonable challenge for the human on a level playing field. The EAW strategic AI doesn't really seem to even show up or grasp what's going on even as it loses dozens of planets.
Yes, I am looking forward to BFME2 next week, collector's edition. It's unlikely that my copy of EAW will see much (any?) more playing time once that comes out.