Most people associate something called "enlightenment" with Buddhism. This is a bit of problem because most people also have some idea of what "enlightenment" means, even though one cannot understand it until one has experienced it. No verbal description can adequately capture.
Also, western culture has a distinct historical tradition, or period, we also call "the enlightenment" that has little if anything to do with the Buddhist idea.
It is better, then, and more accurate, to use "awakening." Soon after his awakening, the Buddha began walking to find his former ascetic companions to explain to them what he had realized. Another person saw the Buddha on the road and asked him who or what he was. He replied, "I am awake," which, in Pali, the language the Buddha's teaching originally got written down in, is "I am Buddha."
So, the Buddha described himself as being "awake," which makes "awakening" a better term for what comes from a sufficiently consistent meditation practice over a sufficient period of time.