One of the ways in which Jewish (and Christian) religion stands out from differing perspectives is the way it conceives of divine-human relations, the relations that obtain between humanity and God. In this uniqueness, I think, can be found a fine argument in favor of the conclusion that they are revealed religions: they are unlike what so many other human groups have in common.
Consider the creation mythology. As I've noted before on my blog, the Israelites' creation mythology in Gen 1-2 stands out when compared to that of, say, their Babylonian neighbors. For instance, in the Atrahasis myth of Babylonia, humanity is created because there is an uprising among the different classes of the gods. The laborer gods get tired of doing hard work for the divinities of the bourgeoisie, so they create man to do all the hard work for them. In Genesis, on the other hand, mankind and everything else is created -- not out of any need on God's part, but simply out of God's goodness, to enjoy life and the creation he has made. God likewise creates humanity in his image so that he can take care of the world and enjoy fellowship with each other as well as with God.
In the case of the Babylonian mythology, the divine-human relations are merely economic. The humans are means used to accomplish the gods' own ends. They are not considered in themselves, but are merely a commodity for resolving labor disputes among different classes of gods. But in Genesis humanity and the creation as a whole is an end in itself, and God cares for it for its own sake. He doesn't need anything from humanity or the creation, since he creates everything ex nihilo. Because he doesn't need anything, his relation to the creation is not based on economic terms, but simply on the basis of his love for what he has made.
Consider also the question of death. Just today, Michael Gilleland posted this fascinating citation about Greek and Indian mythology:
For instance, in one of the poems of the Greek Epic Cycle, the Cypria, it was related that once upon a time Earth was oppressed by the excessive numbers of people milling about on top of her. Zeus took pity on her and conceived the plan of lightening the burden by means of the Trojan War. A similar myth is found in the Mahābhārata. The earth once complained to Brahmā of the ever-increasing weight of mankind, and Brahmā created death to alleviate the problem (M.L. West, Indo-European Poetry and Myth (Oxford: Oxford University Press, 2007), p. 23).
Compare this with the Jewish-Christian story: humans die, not because of some service to a struggling earth, but because they sinned against God and are thus punished; death is a product of guilt and brokenness, not divine concern for impersonal creation. The difference here couldn't be more stark. From a Jewish-Christian perspective, these mythological explanations of the source of death share a common disregard for humanity and exaggerated regard for the creation; they are practices in subtle idolatry, and perhaps even an attempt to avoid recognition of guilt before God.
This uniqueness should not be understated. The notion that God considers the world and humanity as ends in themselves and not as means goes against our tendencies to see everything in terms of reciprocity and payoff. We treat each other as commodities, for the most part, and our relations with one another rarely escape the level of do ut des. The Jewish-Christian theology, however, insists that this is not true with respect to God, and since human beings are created in the image and likeness of God, neither should it be so with us. But what could be more difficult for us than to set aside all calculation and economics in our dealings with each other?! It is hard for us to forgive even small offenses unconditionally; imagine structuring all of our interactions around unconditional benevolence!
Likewise Jewish-Christian theology is unique in that it ascribes so much significance to human moral wrongdoing. Nobody wants to hear this; nobody wants to go around feeling guilty all the time. That is one of the complaints I so often hear against Christianity: it's just a bunch of feeling bad for what you've done all the time. Don Draper says in the pilot episode of Mad Men that there's nothing people want more than to be told that everything is okay with them, that their lives are just fine. Jewish-Christian theology goes squarely against this by blaming death -- the biggest tragedy of all -- on human sin. It doesn't even entertain the nice notion that death was instituted for the sake of the earth, so that at least we can feel good about dying, about easing the burden of the planet. No, not at all: death is a reminder that you're sinful and that you've done wrong against God and against neighbor.
Jewish-Christian theology and mythology go against the human grain; they stand out among religions precisely for this reason. And for precisely this reason, they are that much more likely to be true and revealed, and not inventions.