Given its stress on religious zeal, it would be difficult to find Enlightenment qualities in it. I would say that one particular Enlightenment quality, though, would be its stress on democratic values in that it argued that anyone could receive the word of God. This is an Enlightenment quality because it stresses the democratization of an idea, the ability for anyone to receive an idea. Another Enlightenment idea that is present in the Great Awakening is the assertion of the strength of the individual, in particular, the preacher. Men like Jonathan Edwards were seen as powerful figures during the Great Enlightenment, and with the assertion of the preacher and their abilities, one sees the vaulting of the individual as capacity of greatness, which is an Enlightenment quality.
In a lot of ways, the Great Awakening was opposed to Enlightenment values. Where the Enlightenment stressed scientific thought and reason, the Great Awakening believed in faith in God. But there was one important aspect to Great Awakening thought that was in line with Enlightenment ideas -- the idea that all people were equal.
In the Great Awakening, there was the idea that people should have a direct relationship with God. This said that they did not need to listen to hierarchies placed above them (to ministers or priests). Instead, they should all be equal before God.
This was very much in line with Enlightenment thinking that opposed hierarchy and believed all men were created equal.