In general, I would "weigh in" and say that I tend to agree with Cecil's definitions.
Speaking for myself, I use the term "Biblical" marriage to DEFINE what Patriarchy, properly lived in a loving, servant-headship fashion, SHOULD be. No difference, in other words.
But, in a practical sense, I often prefer the term "patriarchy" simply BECAUSE it is so "un-PC". To say "polygamy" inevitably leads to questions like "ARE you Mormon or Muslim?" -- and confuses the whole issue, since neither are in that sense "Biblical". While the term "polygany" is a bit better, and INCLUDES the fact that a man may have more than one helpmeet, it is generally assumed that such marriages MUST include more than one wife.
"Patriarchy" not only avoids all that confusion, but has the "side benefit" that it allows a bit of additional education. People who want to assume that all Bible-believing men who believe in "headship" must be "the BOSS" (to use Cecil's term) -- or misogynist wife-beaters, to quote the anti-Biblical stereotype -- tend to be a bit taken aback that anyone would actually dare to call themselves such a thing, much less consider it desirable!
The fact that "patriarchal" marriage is BOTH Biblical AND something to be emulated thus often comes as a shock. But so, of course, does what the Bible REALLY says about marriage itself anyway. Somehow I find that the use of the right terminology helps to smooth the path, after that initial hurdle is crossed.
Blessings,
Mark