This discussion will focus on how the passive abilities of different weapon types do not interact with the summoner's skills and mechanics, highlighting how no current weapon type is truly beneficial for the summoner.
- Long bow
A) Heartseeker
It doesn't work with damage-per-second skills, nor with HEX.
B) Bullseye
It doesn't work with damage-per-second skills, nor with HEX.
2. Short bow
A) Arrowstorm
It does not cause HEX to be consumed faster, nor does it have any other beneficial interaction with the summoner's skills.
3. Wand / Book
A) Deadly Finisher
Unfortunately, the "Deadly Finisher" has a very long animation, which slows down the rate at which you consume HEX. And the multiple instances of damage don't cause the HEX to be consumed more efficiently.
B) Echo
It doesn't work with damage-per-second skills, nor with HEX.
C) Perfect Timing
This is a passive that works properly with all skills, however its benefit is quite limited if activated with "spirit shred", "Hex", "Mortal Blast", "Disintegrate", which either already have their own cooldown reduction mechanics, or already have a low cooldown.
D) Conclusion
We can even choose a weapon that best suits us depending on the content we're doing or based on the item's attributes. However, it seems that the passives of all weapons weren't designed to interact with the summoner's skills and mechanics, mainly because most of them don't benefit damage-per-second skills, nor do they make the HEX be consumed faster.