Is it better to use high damage, slower weapons? Or lower damage, faster weapons?

Solution 1:

There is not going to be any solid, 100% always better case for either option, it will depend more on your class and your personal preferences for playstyle.

The biggest piece of information between the two archetypes to keep in mind is that your auto attack cooldown will be ticking even when you're on the other weapon. If you have a ranged weapon with cooldown of X seconds, fire it, then switch your melee weapon with a cooldown less than X, it will always be ready to attack immediately after you fire your ranged weapon and switch to the melee.

If you are using a class that uses a lot of arts, you may want slower but more powerful weapons, to allow the weapon damage (some of) your arts are based off to be higher, and also because you wont be able to use your auto attack cooldown while you're in your art animation (though they will usually be ready by the time the art is finished). If you're a class with fewer arts and more downtime, you most likely want faster weapons so you can more easily micromanage your two weapon auto attack cooldowns.

Solution 2:

This is according to one very big question. Are you going for an infinite overdrive build? If you aren't then slow higher damage usually works out just as well. For infinite overdrive you build bonuses based on hits and skill type chains. If you are using a weapon that has slow CD then your hit gains will be slow and you probably wont keep your chain running fast enough to either gain TP or hit counter. A fast weapon gains more hits and usually has fast art CD's which if you have skills/arts to TP gain on art use results in higher TP faster which can be used to increase the overdrive counter or you can use skill chains to increase hit count/duration. Also faster CDs result in being able to hit secondary and tertiary cooldown bonuses faster and easier. This can REALLY increase your TP gain and damage bonuses based on the bonuses your arts provide.