Not the time but the damage itself. If you test out a weapon with similar DPS but different speed the slower (or faster not really sure right now) weapon tends to give you more damage on your skills. The weapon damage also affects how much damage your skills do. You can check part of this by equipping a weapon then go to the skills section and check the damage done then change to another weapon and see the difference. I want to test this on the field though to see if it is as the damage on skills says.
Edit: This is why a lower dps weapon but that improves your skills damage might be better in a boss fight than a lower dps one. This is my opinion since I haven't tested this as thoroughly as you have.
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