This question is extremely subjective and can only be answered on an individual by individual basis. However, one must examine the sort of life Enkidu lead before he was "civilized."
Enkidu lived without need of luxury in the woods. He was in harmony with the animals, who saw him as one of their own rather than as a threat. He never had to worry about money, social situations (and the headache-inducing drama they can induce), or caring for others. His life seems to have been idyllic, but also lonely.
It is interesting that Enkidu is brought to civilization through sex with a woman and I think the image of sexual union gives us a clue as to what being human means in the context of The Epic of Gilgamesh. The sex is about more than just a good time or even creating more life. It is a bonding experience. To be human is to be a part of human society, a larger framework than oneself. To be human is to love and be loved. And through becoming human, Enkidu finds love and friendship with Gilgamesh.
The two fight monsters together, spend time together, and sometimes even argue. Their bond is the strongest in the whole poem. Enkidu does die as a result of his being civilized, yes, and he even curses the woman who initiated him in one of his lowest moments. However, had Enkidu never been civilized, he would have never found love, the thing which is shown to be the highest civilizing force in the whole of the story. So I would say, Enkidu was not better off before, because he did not have love.