I will tell you about the differences in difficulty, they are small but matter. In easy, the enemy gets the hard modifiers and vice-versa.

Easy +20% damage taken (Yes you take MORE damage in easy mode due to a bug) +20% damage dealt +20% movespeed -20% delay between shots -20% cost -20% build time (faster)

Hard -20% damage taken (yes you take less damage in hard mode) -20% damage dealt -20% move speed -20% delay between shots +20% build time (slower)

Harder can sometimes be easier, especially with infantry combat due to the armor bug.  Tanya in hard mode will kill infantry in a single shot, while in easy she doesnt.  
Also since tanks build slower, you do not have to click buildings/units as fast during combat.
 The armor bug greatly affects V2 Rockets and air units.  V2s cannot destroy power plants and pillboxes with a single rocket in easy mode.