Atack speed, overall damage and damage per second. On what should i focus on?

When comparing weapons i have this green/red number.
This weapon will improve your overall dps but does it mean it is an upgrade?
My rifle increases my attack speed by 43% and physical damage by 83%.
It is a level 25 weapon.
When checking weapons with higher level i always get info it will do less dps but when I check the damage in the second tab those higher-level weapons will do more damage.
So is sticking with a faster weapon optimal solution so i will get more hits or is it better to have harder harder-hitting weapon a better solution since my skills will benefit from it more?
Thanks for the info,
Cheers

From this post I assume you are a newer player. I would recommend trying to find builds and guides from the forum, grim tools or videos.
The stats you need, depends on what your target build is. If you want a pet build none of those stats make sense. If you are a physical spellcaster go for extra physical damage. If you build a default attack/chance on attack build, then go for the attack speed (it is capped at +100%).
The ‘damage per second’ stat does not describe, how good a weapon is, just tells the damage done by default attacks and their modifiers.

2nd Tab shows damage per attack, not per second.
Attack speed can make a massive difference for DPS, not just stats like the 43% bonus on your weapon, but also the base speed of the weapon.

Eventually you will want to max out the attack speed to the point where you reach 200% in the second tab, if possible.
How much extra atk speed you need for that depends on the base speed of the weapon.

Meanwhile, if you get other sources of atk speed or total speed, from gloves, rings, amulet, devotions and some skills, you won’t rely as much on the boost from your weapon and other weapons might look better in comparison.

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