Now this discussion isn't directly a "who would win in a fight" but more of a question about comparing them.
Gilgamesh is stated the most powerful heroic spirit, Enkidu is his equal in that respective.
But is he an equal in every class or just in general, as we know Gilgamesh and Enkidu both have different classes apart of them.
Enkidu's main classes are Lancer (post Shamhat) and Berserker (pre Shamhat).
In Strange Fake it's said that if Enkidu was summoned in his Berserker Class he would basically have been summoned with the power of a God. At least in my interpretation, they are saying as a Berserker he would of been summoned with more power than he is as a Lancer.
Generally that fits into the Lore of before he became a humanoid he was a monster who was made with the full power of Anu (A Chief God probably) and Aruru (A Creation and Mother Goddess).
(Absolute Demonic Front - Section 1: In the Age of the Gods)
But during the battle with Gilgamesh, it's noted that it was Gilgamesh's first time using Gate of Babylon. As well as being one of the first times he encounters an equal, likely meaning first time he ever fought that hard.
Humanoid Enkidu fought a inexperienced Gilgamesh and they tied/I might give it to Gilgamesh (but that's not important)
After they had fought they became friends and collected more treasures and gained more experience within their own myth and in Fate.
So wouldn't that imply that Post Battle Gilgamesh who even collected treasures after Enkidu's death (even making Enkidu one of his treasures) should be above Enkidu? As now he became more experienced and weapons to actually fight with. (Enkidu may have become stronger, but generally Gilgamesh seems to have gained more off of their adventures.)
Now off of that, would Berserker Enkidu be above Gilgamesh? If before he became humanoid it's stated he "MIGHT" surpass the King of Heroes. While it was still an inexperienced and before some of his biggest accomplishment’s?
Fate/strange Fake Volume 1 - Prologue VI: "Lancer"
It's a strange question I ask myself, especially since now we even got a Ruler Gilgamesh, yet still haven't even seen Berserker Enkidu.
(Also if anyone's feeling silly. Enkidu Pre (Shamhat) vs Gugalanna. As Enkidu is stated to be the Most Powerful Noble Phantasm with a living will, and Gugalanna is also a Noble Phantasm. But also possesses the "Most powerful Sumerian Divine Spirit" claim.)