It's pretty simple, honestly. +Damage adds directly to your Weapon so if you have a 44-52 Damage weapon (random values, hooray!), it now deals 47-58. This value is then multiplied by (1 + DEX/100) or 6.15 for you. This comes to around 323 AvgDmg.
Now, +23 DEX here insteads means you have that 44-52 Damage weapon with 538 DEX or a 6.38 multiplier. This comes to around 306 AvgDmg.
Edit: Basically, just think of it like this:
(Weapon Average Damage + Ring Damage) * (1 + Stat/100)
As Weapon Damage grows, that Ring Damage starts getting worth less and less even as your Stat grows. 1000 -> 1023 DEX on a weapon that hits for 500 is just better than 1000 DEX on a weapon that now hits for 504. Early game, +Damage is worth a lot for your total damage; late game, Stats are worth a lot.