I've asked this like 4 times basically and no one's really answered.
From what I've been able to piece together from in-game stuff though:
If you look at the Aux effects, to the right of bleed and poison, there's a white circle, and a black circle. This represents "divine" and "dark" power, and the number by it (when there is a number) should be thought of as being similar to the number a weapon has next to "critical" meaning if it's 110, then when it's doing the damage that corresponds to, it's actually doing 110% damage instead of a normal 100% damage.
Divine weapons have the white circle, usually at 110. This seems to mean two things: bonus damage against evil undead stuff like I guess skeletons and stuff, and also if you kill said skeletons with such a weapon that normally come back to life before killing the corresponding necromancer, they will stay down even with the necromancer still alive.
Occult weapons, on the other hand, I don't know a lot about. Some have claimed it saps HP from your enemies. I never managed to produce such effect in my tests with the occult club. However, the description for the Dark Ember seems to suggest maybe it does bonus damage to godly and human enemies.
I am snazzier, hot, hot rant. Warily slight as. Croak rush, OK? Weirder, almighty make out. ::)
Extra damage to holy/Gwyn-related? That's an.. .interesting bonus. There's a practical purpose for holy, since it stop skeletons from reviving (regardless of any damage bonus). I'm pretty sure fire weapons would do more damage to skeletons, outside of the reviving, so that's an important effect in a way.
Silver-knights are pretty specific (I'd assume the dark knights too, since they're Gwyn's knights.. and they were originally silver and just got charred). Aside from that... clerics, holy people? Gwyndolin? Gwyn himself?
How much of a damage bonus are we talking? You might be able to get an occult and enchanted version of the same weapon to have roughly equivalent stats to test it.
I have +9 divine long sword and +5 occult long sword. Occult one does better against dark knights for sure. I'd say about 20% better. Now it's not a good representation because divine is not at +10 but the bonus id get for it for +10 does not look that significant.
So yeah. If you want I can go and get definite numbers right now while I'm still up.
Well, the modifiers are different on Occult/divine/magic/enchanted (and the damage types are different on everything else).
A good test would need to account for that. I was thinking an enchanted and occult might be able to hit roughly the same damage levels, and with someone that had no points in int/faith, would probably have negligible effect on modifiers. You'd also want it to be the same weapon (like.. a short sword or whatever), and the same hit type (hitting someone right after they get staggered on your block does more damage than an average swing. Backstabs, etc. are also different.