There's three ancient Greek words you do not see every day! They are, however, extremely relevant to understanding what most Christians believe today in our history, and will lead us to a rather key question regarding the belief that prevailed; I will be asking both Stephen Holmes and Bart Ehrman for their points of view on this question (maybe I'll bug Dale Tuggy again too, but I am still waiting for another answer from him, so don't want to bug him too much). But first, let's define.
Homoousian is the belief-set that Jesus is of the same substance or essence as God the father [the one and only divine].
Homoiousian is the belief-set that Jesus is of similar substance or essence as God the father.
Homoian rejects any talk of substance with "its materialistic overtones, inevitably misleading and unhelpful" (Holmes, Quest For the Trinity, p 93), but still keeps the key iota there, that Jesus is like God.
In Holmes' book, the Homoiousian and Homoian distinction is not clearly developed, with Holmes concentrating mainly on the predominant Homoian belief in the fourth century. I am not sure why that is, and Wikipedia, for instance, is able to cite many more Homoiousians than Homoians - I suspect that the distinction is fine and not exclusive. What is fascinating is that in the fourth century, when these first monumental councils and creeds were coming together, it is not the Homoousian view that initially prevailed. Furthermore, the Roman Emperor Constantine who was absolutely pivotal in the 325 Council formation, was baptised several decades later by a Homoian (or Homoiousian) bishop, just before he died! It was by no means a foregone conclusion (Ehrman) that the Homoousians were going to win out, but in the end they did.
And so we get closer to our question - why was that? When I read Holmes' couple of chapters on this key period, and remember that Holmes is a deep and devout believer himself in God's sovereignty in this process, he points to a lack of unity among the Homoians. They were also too busy trying to dismantle the opposing view, without "doing theology" themselves. In the meantime, the Homoousians were very busy doing theology. Somehow, I still do not quite get it.
I am not certain that Ehrman's orthoparadoxes idea quite answers it either - this is Ehrman's idea that what prevailed was where certain "right" (ortho) beliefs of one belief-set were maintained and others rejected from several different 2nd and 3rd century Fathers, none of which were fully orthodox (and some, like Origen, positively condemned later), in order to gain a paradoxically, but ultimately purely orthodox view.
So let's see if I get lucky with some answers...