I may be misremembering, but I don't think there was any difference between the Hawk Blade and Ember Blade in the game. I think it was a missed opportunity, at least from a narrative view, to have something detailing the difference between the two. I could imagine the Ember Blade being sheathed in flame, while the Hawk Blade pierces the sky with a shrill, falcon scream with each strike.
I admit, this is one of those world-building details I like to come across, so others may not care
