Hi , I noticed something, but not sure if i am right: AI tied to command rank of general too. When you fight vs army with high ranked general, such as mongol generals, you can easy lose in open battle. there is no difference if your army dont have general or have 10 stars general, cause you are commander. Get army with negative morale penalty general , and you will also see difference.
Also, only the cool fights in M2tw are in very early period or vs Mongols or Timurids, if they dont get assassinated before.
Last thing - it is true that campaign difficulty affects all aspects, including battles. I will try H/VH from now. May be i am mistaken, but it may be harder then VH/VH.