First blood on the same initiative step
When you have two simultaneous effects that need an order to resolve, the active player gets to decide the order.  So the player whose turn it was would probably choose themselves to receive the point for First Blood (though they could choose which either player to get it). 

Alternatively if it's a friendly game you and your opponent might agree that both players score First Blood, or that neither player got it. Or even that it hasn't been scored yet.

That said there are several variants of First Blood out there since it almost always goes to the first player. Last Blood is fairly popular, where to score it you have to kill a unit and then not lose a unit on the opponent's turn. 

This question has given an alternative idea which I plan on implementing when I can get my opponent's permission. I'm going to make a "Blood Trophy" and the first unit to kill another earns the Trophy. However if a unit kills the unit that controls the trophy, they gain the trophy. Whichever army controls the trophy at the end of the gain gets a victory point.