The crystal upgrade path is normally a 10% increase in AR for the scaling weapon, it increases base damage, but does not affect scaling. However, bows are a unique case because they are granted a 60% increase in AR.
If you take at look at this: Comparison. You'll notice that Maxed Crystal Bows are on par with regular large weapons (Ultra Greatswords and Great Clubs) while they will outclass any other melee weapon, even their crystal versions.
Crystal Bows = Quick, ranged UGS and Great Clubs. Imagine the headshots!
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