The first thing to check would be if Player is attacking and Enemy is not attacking, it's simple enough, if there is a collision, it's the Player who is attacking.
Now if both are attacking, and if their attack motions take the same time, the one who started the attack first would be the one who "wins", i.e. the one who is tagged as attacking.
And if their attack motions do not take the same time, you could check who's closer to the end, percentage-wise, and tag that entity as the one performing the attack.
That being said, there is nothing preventing you to consider both as attacking if they're in an attack motion.
Another thing to consider: what part of an entity hit what part of the other entity? An axe could be split into two parts: the blade (the part that actually performs the attack) and the rest. If the player's blade is in an attack motion, and it hits an enemy's axe (which is also in an attack motion) on "the rest" part, then the enemy attacked too fast or not fast enough, while the player found a sweet spot: the player is tagged as attacking.