Amulet with higher Level skill but deal less damage

As you see in the 2 pictures below, the left-hand side amulet has +2 level skill of all melee skills, while the right one has +3. Both do not have any increased damage modifiers except the plus level skill, but the +2 has much overall damage than the +3. I'm not sure this is a bug or something. Could dev or support team please check this for me? Thank you.

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Rilakkyuma#4193 wrote:

Both do not have any increased damage modifiers except the plus level skill, but the +2 has much overall damage than the +3.

The +Strength modifier on the second amulet is an important difference.
Equipping the second amulet increases your Strength, which in turn increases your maximum Life. Your current Life will not rise to match your new maximum Life--you will be missing Life until Life regen fills the gap, you use a Life Flask or well, etc.

The passives Initiative and Killer Instinct give you increased damage while on Full Life.
You're temporarily losing their bonus on equipping the second amulet. Try using a Life Flask after equipping it.