Note:
Lv50 skillbooks can replace the following stigmas, they share a cooldown.
For example, Asmo Chanters get the lv50 skillbook "Aether Spell" that is the same as the stigma "Curtain of Aether" but "only"* reduces 50% of incoming damage but costs less mana. Both share a cooldown so you can only ever use 1 of them. Meanwhile the skillbook versions are slightly weaker, it is better to conserve a stigma slot. The following stigmas are just for explanatory reasons, see them as the lv50 skillbook versions and you get the same differences.
*it's actually better this way as it depletes the 5000 shield-points slower than the 60% stigma version
Sorcerers are an exception to this with lv44 stigmas "boon of strength/quickness".
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Class: Cleric
(balanced) (difference: 3 eHP)
Elyos: Yustiels Splendor
1403 Heal + 1400 Heal over Time (HoT)
Asmo: Marchutans Splendor
1403 Heal + 1403 Shield
Class: Templar
(Elyos Templars are stronger)
Elyos: Punishment of Light 1
907-911 dmg
2 seconds Stun
Asmo: Punishment of Darkness 1
907-911 dmg
50% absorb (self-heal for 455 HP)
Class: Glad
(Asmo Glads are stronger)
Elyos: Shattering Wave 1
443-447 dmg
15 meter range (ranged attack)
18 enemys
10 meter AoE radius (from the target)
-600 def / 30s debuff
Asmo: Piercing Rupture 1
1081-1085 dmg
0 meter range (meelee attack)
18 enemys
10 meter AoE radius (from yourself)
-600 def / 30s debuff
Class: Chanter
(Elyos Chanters are stronger)
Elyos: Divine Curtain 1
5000 Shield +2240 Heal over Time (HoT)
50% of dmg taken will be shielded
6 allies, 20 meter range, 15 seconds
Asmo: Curtain of Aether 1
5000 Shield
60% of dmg taken will be shielded (which is worse because it depletes the shield points faster)
6 allies, 20 meter range, 15 seconds
Class: Assasin
(Elyos Assasins are stronger)
Elyos: Divine Rune 1
explodes 5 runes
20 meters range, 1 target
+silence debuff
+ attack speed reduction debuff
Asmo: Rune Swipe 1
explodes 5 runes
20 meters range, 1 target
X% absorb (self-heal for some HP)
Class: Sorcerer
(debatable - Elyos sorcs hit harder and more precise, getting through enemy Mress, Asmo sorcs can turn on chaingun mode and just blast away all their mana - I'd say Asmo sorcs are getting the better deal here)
Elyos: Boon of Strength 1
+500 magic boost
+500 magic accuracy
15 seconds
Asmo: Boon of Quickness 1
50% casting time reduction (turbo fast casting)
15 seconds
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As for Rangers, both seem the same in this patch, correct me if I'm wrong.
As for Spirit Masters, Elyos summon a Tempest Spirit while Asmos summon a Magma Spirit. Which of both is stronger? Only SM players may know.