I guess I'd have to ask you to specifically identify what you mean by, "the major branches of Christianity."
And then I would likely bow out on some for now, because it has been some time since I studied various soteriologies, so I wouldn't want to misspeak.
I will say something re: something a bit closer to home for me: After a lot of work in study and some pains in coming to grips with my updated view some time ago, I came to view the soteriology I was trained under as likely and unintentionally (in most) marching many off a cliff. This view was shared by another in that camp who studied the matter with me and I don't think we pushed our conclusion on one another, but each of us saw things from Scripture that caught us both a bit off-guard at times.
Any such discussion would have to include what is included in the word "salvation," which is another big piece that typically gets intense in repeated discussions from time to time on other threads here.
Additionally, as I said earlier in a post to chevyontheriver, although once staunchly in the camp(s) opposed to the so-labeled Catholic "works-salvation" gospel, I have found in some of these threads in discussions with Catholics, that their gospel as they explain it does not seem to be in actuality what I was taught it is. Also, I find some of such discussions to present a salvation that I see conforming to Scripture in ways that have pleasantly surprised me a bit.
I'm not speaking comprehensively, but just trying to answer you in part. To truly discuss this I'd want to take any soteriology point-by-point and bring out Scripture to address them all. I'm cautious at this point of just dismissing a camp under some label that may or may not be comprehensively valid.
Hope this makes sense.