For GS the only difference I see is the status of the item, p.attack and attack speed.
Your passive skill Superior Skill Mastery is "skill power + 15%", so the more p.attack you have, the more damage it will cause to Skill, so Bow is the sensible choice.
But Bow does not have the same attack speed as the Crossbow ...
Now I will speak for myself, that I am Yul Trickster ...
Having a Bow for me does not mean anything, because my Passive Superior Instinct Mastery skill says I have +15% p.attack using crossbow ...
As I have a Kelbim Crossbow ... His p.attack is 1,434, + 15% = 1,649, higher than the Kelbim Bow of 1,592. And as I said before, the difference that remains is the attack speed, of which the crossbow is larger.