The adepts weapons have two advantages but they are very minor.
One is it allows for adept mods, such as adept icuras, adept range and adept big ones. While these do give good stat boosts they aren't strong enough to break adept weapons causing them to be "must use this adept weapon in the raid or kicked".
Seconds advantage, when you masterwork an adept weapon it gives you a +3 stat boost in all stats while the master work will get its additional +10. For example, if the masterwork is range and a weapon has 50 for a range stat, once you've fully upgraded the weapon the range will increase to 63. While the others just upgrade by +3.
A lot of inexperienced players believe adept weapons are broken because they allow for adept big ones and they have a misconception they are the best dps weapons for example reeds regret adept. A lot of players complained about it being the best pve weapon locked behind trials. Yet the damage output isn't that much higher than a normal threaded needle.
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Crafted weapons also get that +3 boost at level 20.
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Yeah that's true but they are different from adepts. Crafted weapons aren't broken even tho they are far better than adepts thanks to enhanced perks