Who finally wins the conflict between Gawain and Green Knight in Sir Gawain and the Green Knight, and why do you think so?

The events in Fitt IV can't really be called a conflict in martial terms. It is more apt to say "contest." The winner of the contest is, of course, the Green Knight, who wins for several reasons: (1) The Green Knight is magic; (2) he has the whole contest plotted out; (3) Gwain is noble and pure with only one failing.

The Green Knight, outmatching Sir Gawain by a huge degree, has the physical prowess to beat Sir Gawain regardless of any other circumstances, bu it turns out that (1) the Green Knight is the servant of Morgan le Fay, a sorceress and the half-sister of King Arthur, who planned the whole contest.

(2) As such, the Lord of the castle, who is the same man as the Green Knight, has plotted all the temptations out with his wife, who played a part toward Sir Gawain and was not sincerely seeking to seduce him. (3) Sir Gawain shows the Lady only one failing: he accepts the green girdle from her because she tells him that it preserves life. Gawain relents after his first refusals and accepts the green girdle because he is, in fact, frightened of standing up against the Green Knight.

However, having said the above, it is also true that in a metaphysical sense, Gawain is the victor in the contest because he proves that he is a pure and noble knight. In fact, the Green Knight names him the "finest man alive" whose one fault stems "understandably from his love of life." Gawain learns a lesson, to shun the "frailty of the human flesh" and returns to Camelot to share his story. This is very different from our society that shuns, and often disparages, the values of purity and nobleness while going to great extremes to embrace to the opposites of these.