I've always gotten the impression, since the BSG days, that the gods of the colonies are to the ancient Greek gods of Earth as the modern Christian concept of God is to the Old Testament God. More civilized!
I think that generally speaking you're really onto to something here DB, and again, generally speaking, I agree with you. If the pagan gods had been around for literally thousands and thousands of years and had never really been challenged by a competing religious ideal, and yet man had continued his process of civilization outside the direct influence of the gods, then you can expect that the concepts regarding the nature of the gods themselves would correspondingly change. Not so much by direct competition, though I'm not so sure some kind of underground monotheistic impulse has existed for a long time in the colonies, but by a slow, gradual process of evolution.
(I really wasn't arguing that the gods of the Colonies were the direct present-day corollaries of the ancient Greek gods, merely that they had retained vestiges of ancient and violent pagan impulses regarding such things as Bacchanalia and human sacrifice, etc. which could be clearly seen in the early holoband/Virtual World scenes. That is to say the gods had retained their early nature myths (psychological nature), but overlaying those had developed, over time, a civilizing myth, or a sort of veneer of civilization which is far more sophisticated than that of the more ancient incarnations of the gods.)
For instance the prophecies that kept surfacing in BSG seemed to me far more like the Old Testament prophecies of the prophets (looking dozens, hundreds, or even possibly thousands of years into the future, and concerned with the grand-scope and overall sweep of historical human events) than the more tactically targeted utterings of the Oracle of Delhi, which were almost always designed to address smaller and more specific problems. The Old testament prophets tended to speak on matters that were often cosmic, long term, and strategic (or at elates this is the way they were often interpreted), whereas Oracles usually addressed specific questions of a more local and tactical nature.
Yet the Pythian prophecies in BSG seemed to me far more sophisticated than a typical oracular reply, rather they seemed a coherent and cosmic prophecy of long term import and effect. The reason, I think, is that over time the gods transformed in nature from being squabbling, violent, self-involved mythological representations of individual character-personas, and more into "guardians and advisors and defender of peoples." In transforming over time to become more civilized their focus shifted from pursuits of personal power and interest to become more cosmic and grand in scope and shape. In other words the gods began to grow up (and in some ways I think they outgrew the Men of the Colonies who although they become more civilized and sophisticated, also retained far too much of their strictly more primitive nature).
I think then what you really have going on in BSG and in Caprica (religiously speaking) is the concept of the evolution of the gods and the parallel development of the monotheistic ideal of the One God form an underground religious force to serious contender for both "what really constitutes the nature of God, and what really constitutes the higher nature of man and civilized man." Over time the gods have become "civilized" as man has become civilized, and correspondingly the One God is only now becoming fleshed out in nature (still in an underground but nevertheless more public way).
(I have a personal theory that in interactions between God and man the perception of how God is envisioned and perceived is partially a reflection of how God presents himself, and partially a reflection of how man attempts to and wants to perceive God's nature. So how man perceives God, and in this case I'd bet how cylons perceive God is a sort of fluid suspension of God's nature and how man can, or will, or maybe both, perceive that nature.)
So to me as far as the One God ideal in Caprica is being formulated, you have conflicting ideas about the nature of God. On is that God is love and mercy, the other is that God is power and justice. These two natures are in conflict (this conflict is in my opinion not a necessary conflict, but from a human perspective it is an often understandable conflict), as far as the followers of God go, and these various followers are wrestling, as indeed in many respects the real world is and always has been, over what is the truer and more important nature of God. And that will determine how God is both perceived and presented.
And I think these ideas about God are intimately related to the nature of the cylons, the ideas surrounding technology and what role it plays, and the concept of the soul, human and cylon. For I can easily see, if the Cylons end up being irreproducibly analog in nature and in rebellion against men who they consider oppressors that they would then gravitate to the idea of a single, supreme God, and in that respect one must also remember how big a role numbers played in BSG, as regards the gods, the way in which technology functioned, the prophecies, and for the cylons and the followers of the One God. The cylons and Baltar's group were awfully close in many respects. Especially metaphysically.
But, and this is off the subject, speaking of the soul, the mind, technology, and numbers, it has interested me very much so far that Zoë has made no attempt whatsoever to really contact her father once she was emplaced within the body (or coprus) of the Cylon. She could as easily communicate with her father, through technological interface, as she could with her "boyfriend." But chooses not to. I think she has a very good reason for this. Or I should say very good reasons, and that she suspects far more than she has yet to let on.
Another thing I never really thought about before in this respect is the netflow of data signifying cylon thought processes. It is of a red that resembles fresh blood. It could have been of any color, but it matches the eye and looks like fresh, bright blood.