Each school of Buddhism believes the states it describes is Supreme enlightenment, Interestingly the Buddhists believe in saying that all the other schools are right but we are just a bit more right and thus we deserve the title Supreme for our conception of enlightenment. But as you look at the sutras for the various schools you really see that they did make progress, and the conception of the nature of enlightenment kept evolving and getting more subtle all the time. A lot of Buddhism has to be re-evaluated now that the texts preserved in Tibet but not elsewhere are translated and come to light.
So when we say supreme enlightenment you have to decide what group discusses supreme enlightenment. But it is fairly clear that from a philosophical stand point it is Hua Yen buddhism of Fa Tsang outside Tibet. Within tibet it is probably the commentaries of Mipham that deserve a close look, but I do not know much about this area. I particularly like Dzong Ka Pa because he said that reason had a role in enlightenment which is something I have thought for a long time. How can it be the middle way if it excludes anything? But amazingly Dzong Ka Pa did not believe that consciousness was reflective and so that is a major disconnect which Mipham tries to remedy.
In Tibet you get DzogChen which claims to be the supreme teaching but is really a heresy of Buddhism because it erases the difference between the two truths, and is a lot like Zen Buddhism to my mind.
But if we stick to Buddhism proper, and discount the heresies, and consider Fa Tsang’s work the pinnacle in Hua Yen as the pinnacle then we can say that the unique quality of the one who attains supreme enlightenment would be the realization of emptiness as interpenetration of all things.
A good book about that is
Hua-Yen Buddhism: The Jewel Net of Indra by Francis Cook