Bulwark of Dawn opposite direction 2739 -> 2648. Sorry

Check the runes of ur spells, maybe they convert dmg Type A to Type B and you have more % increase for dmg Type A instead of B

but average dmg in tooltip should then also increase, in particular the second ring is nearly the same but with much more better stats

No it should not, if you increase ur dmg Type B by more % than Type A it will be deacreased.
For example i have +50% physical damage and tons of % material damge.
Im dealing less dmg with rend/toxic compared to physical simple because of the 50% inc physical damage

I dont understand you. The total dmg in tool tips also decrease, on second ring I have 4% more occult dmg and total dmg on all skills decrease.

For example Bulwark of Dawn:

holy dmg: 1166 - 1367 -> 1159 - 1331
lightning: 274 - 363 -> 218 - 266 but second ring does more lightning dmg

Everything is weaker but the second ring is better?

Yeah well, i just noticed that im sorry, i missunderstood you.
Are you sure that the damage is "to spells" on both rings?

Yeah, it is "to spells" on both rings :-(

You should not use the character sheet DPS as any information about what type of dmg u do.

You have to check each spell individually to see what type of damage increase you get from each ring.
However it can be the case of the ailment damage on frost is higher then on lightning because on first ring frost is the higher number and on 2nd ring lightning is higher.

The way ailment damage work in Wolcen is

Each spell has a base element type of damage associated with it (also depending on rune choice)

Example 1 - Anomaly has stasis as base damage type , but it can be altered to Lightning via a rune.

Now with a specific node in the skill tree you can be allowed to apply 2 types of ailments per spell used

Example 2 - Using your first ring (and no other + x type dmg to spells) your anomaly will now do Stasis + Frost damage instead of only Stasis.

Example 3 - Using the second ring (and no other + x type dmg to spells) your anomaly will now do Stasis + Lightning damage instead of Stasis + Frost.

So possibly you have some piece of equipment that increases your frost damage % ring 1 could do more damage then ring 2 even tho higher stats on 2nd ring.

Just an example and there might be a whole other reason or possibly just the character sheet damage is still bugged (which i think it has been since day 1 )

All of my skills decrease in dmg (Anomaly, Tear of Etheliel, Bulwark of Dawn, ...). The second ring is clearly better, but I do fewer average dmg. I dont get it. For Tear of Etheliel: I took the rune which converts to fire dmg, thats all. Can someone explain whats going on here? It is just frustrating and makes no fun at all. Overall a great game, but this is just annoying.

Also I dont have specific "frost dmg items"...

And the "+15% holy dmg stone" is nowhere visible.

So I tried different runes and skills and passives... no change at all :(