Axe Lord

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Hello,
First of all, sorry but english is the language in which i play this game so i tried to translate all the terms the best i could but some are hard to find.
So i am a DM and in my group there is an Half-elf Summoner (Archetype synthesist) and an half-orc Barbarian both level 5.
And for sometimes now my Barbarian has been complaining because the summoner's eidolon was doing most of the close combat damage even when the barbarian is in rage mode.
Let me give you some stats:

So first of all The summoner has an evolution pool of 11:
8 (base)
+1 (1/4 every level since he is an half elf)
+2 ( he took the feat "extra evolution" twice)
Which means he took a biped eidolon with:
-Ability increase (strength):2
-Energy Attacks (acid):2
-Limbs (arms):2
-Improved Natural Armor twice : 2X1 = 2
-Claws :1
-Improved Damage (claws):1
-Bleed:1
Total : 11 everything seems legit
Which means that his eidolon has a
Str: 16 (base) +2 (strength bonus lvl5) +2 (evolution) +1 (Ability score increase lvl5) = 21
AC : 10(base) +2 (natural armor) +4 (armor bonus lvl5) +4 (evolutions) +2 (dex=14) +1 (feat "dodge") = 23
ATT: 4 claws attacks with the bonus = 4 (base) +5 (strength) = +9
Damage : 4X(1D6 +5 (strength) +1D6(energy attacks))+ 1D6 (bleed)
= 29 (min) -74 (max) (if all attach touch of course)

And now the Barbarian during rage:
Str: 18 (base) +4 (rage)= 22
CA: 10 (base) +7 (breastplate+1) +3 (dex=15) +1 (amulet of Natural Armor) +1 (Bracers of armor) +1 (feat "dodge") -2 (rage) = 21
ATT: 1 "Great Axe +1" attack with bonus = 5(base) +6 (strength) +1 (weapon+1) +1 (feat "weapon focus") = +13
Damage : 1X(1D12 +6 (strength) +1(weapon) + 1(feat "martial focus")
= 9 (min) -20 (max)

As you can see the two have equal AC but even if the barbarian as a +4 chance of touching the enemy the damage from the eidolon is just massively greater (3 to 4 time greater) which infuriate my barbarian

So i m asking this question, Am i missing something here ? or is the eidolon just super overpowered ? or is the Barbarian not build well enought ?
Thanks for your advice