The issue here is not the whole book of Genesis, but just the first few chapters. The book is actually a compilation of several writings preserved and assembled at various points. It is widely believed across most Christian traditions that most of the book is literal historical fact.
The issue you've heard rumblings of stems from the first couple chapters, specifically the creation story. There are several major views on this and how it is interpreted depends on how different factors are weighed. The issue is certainly large enough that it would be impossible to generalize across all of Christianity.
However, the breakdown is not quite as easy as your question makes out, because it isn't a split over history vs. parable. Those are two ends of the spectrum, but most of the major denominations are going to fall somewhere between those two extremes.
I am not going to detail the positions of all the views, but I want to give you a few terms and groupings that will help any further research you do on this issue. First you have your Young Earth Creationists. These folks are going to be roughly what you would classify as "literal historical" in that they read words like "day" at face value as something equivalent to our 24 hours. You also have Old Earth Creationists who believe that the creation account is literal history but that "day" might mean "age" and so we don't have a frame of reference for how long each thing took. Please understand I'm painting with very broad stokes here. In between those, you also have something called the Framework view that takes the Genesis account quite literally, but does some textual gymnastics, classifies the writing as a kind of poetry that we've lost the key to, and puts it all back together in a different order. In a way you could call this "parable" in that the text is trying to give us the gist of what happened without being scientific about the details. However this view is actually not the extreme that you probably hear rumored. Farther out lies the Theistic Evolution view that really discounts the entire creation process except for allowing that God put some sort of evolution in motion and possibly kept it on track. This sort of view must necessarily discount the text as a fictional rendering inspired for some purpose other than to tell us about the actual origins of the universe.
Given those major viewpoints (and bearing in mind that there are lots of minor modifications), some generalizations can be drawn about denominations and their views, but it is remarkably hard to do so with any level of meaning when most of the major denominations are actually showing fracture lines along the issue. Some openly embrace multiple positions, some are fighting a loosing battle to claim a single position. Only in smaller (and thus kind of too specific to list here) denominations are there consistently held positions on this matter.