How does Enkidu act as Gilgamesh's alter ego? In what ways are their personalities similiar? In what ways are their personalities different?
An interesting cluster of questions.
They are both warriors, both powerful, both adventurers. They become inseparable, like good brothers or classic friends.
They differ in that Gilgamesh seems, at the poem's start, like he feels entitled. He is the ruler, yes, but he's abusing his power. His weaknesses are the weaknesses of royalty.
Enkidu, by contrast, is the wild man. He rages around wildly, so that his weaknesses are the weaknesses of the animal in man. You might say that together they are the perfect hero: civilized man and animal man.
However, there's more than that. Enki was a god of balance and of the earth, and he creates Enkidu to balance Gilgamesh.
Enkidu is also the part of Gilgamesh that dies, and that teaches him thereby the meaning of life.
(Their links end up being more symbolic than based on personality.)