When a unit counter attacks does its attack stat determine the likely hood of a successful counter attack or does its defense state determine it? Likewise does the defense stat of a attacking unit reduce the likely hood of receiving a successful counter attack? I am relatively new to the game(~90 hours) and am not certain exactly how this mechanic works.

I believe it's the former (the attack stat).

If I'm not mistaken, something very similar has been discussed here : https://www.games2gether.com/#/endless-legend/forum/6-game-design/thread/3569-an-explanation-of-the-new-combat-system

It's always the relationship between attack (by hit) and defense (to prevent succesfull hit) stats of involved units.