If anything, I see a war splitting the Fed and unifying the Klingons, as has already been discussed - at length - here.
Personally, I don't see a war causing any kind of fracturing/splintering/infighting/etc. for either the Klingons OR the Feds.
The civil war we saw in "Redemption" came about, at least in part, due to a split between those who thought the alliance with the UFP was a good thing, and those who thought the exact opposite. However, in the YE timeline, there's never an alliance in the first place; with no heroic Ent-C sacrifice to sway them, the tensions between the Klingons and UFP grow to a boiling point, and eventually spill over into war. In that scenario, the Duras family would probably be simply another powerful Klingon family. No doubt they would be at the forefront of the war, given both their power and their
particular disdain for the Feds, but their views wouldn't be challenged since there's no "pro-Fed" sentiments from ANY of the Empire's houses in that timeline.
As for the UFP... Dominion War. Granted, it was considerably shorter, but even so, it was certainly no less bloody, and there was not a single inkling of any UFP members threatening to secede or making noises about the war being a mistake or what have you. Now, I have no doubt that some sentiments along those lines at least
existed here and there throughout the UFP; with a society this large and diverse, it is inevitable that some people are going to disagree with some decisions that the larger government makes, especially in the context of a war. But on a scale that was anywhere near large enough to threaten the UFP's existence, or make any difference in Starfleet's ability to fight the war? No sign of such a thing. Even with a prolonged war like the one in YE, I see no evidence in the body of filmed Trek to suggest that such a thing would happen. Given that the UFP are generally not the aggressors, it is likely that whatever caused the war was due to misunderstanding or pure Klingon belligerence (see: late season 4/early season 5 DS9, where the Klingons almost start a war with the Feds because they decided that these worlds that had belonged to the Feds for almost a century suddenly needed to be back in Klingon hands. Granted, the Martok changeling spurred that plan forward, but it wasn't exactly difficult to get Gowron and the rest of the Empire's leaders to go along with it), which would make most UFP members more determined to defend themselves (since that's how they would probably view the war, as a defense against Klingon aggression).
Different timeline, it does not count for this discussion IMO. We have no way of knowing what was going on in that timeline. In this timeline the Klingons even admit that they would not win a war with the federation.
Unless there is another such mention by a Klingon character of how a UFP/KE conflict would go, mentions of the Klingons themselves "admitting" that they wouldn't win are references to Kurn's lines in DS9 "Sons of Mogh", yes? That was season 4 of DS9. The UFP had already improved its defensive position by then, to a VERY large degree, compared to the time frame of YE: we have the Defiant and Akira classes, the UFP has already had experience fighting the Dominion and the Borg, and the Sovereign is on the way. Others in this thread have cited those very factors, which improve Starfleet's combat capability during the late 2360's/early 2370's, as reasons why the UFP might win. Well, it works the other way too: Kurn's statement refers to the UFP
at that time.
You'll find that YE is indeed relevant for this discussion. We are talking about a hypothetical Klingon-Federation War and YE shows us what such a war would be like. There is no mention of the Klingons or the Federation having allies in the YE war, just Klingons fighting the Federation, with the Federation loosing. Also, Starfleet appears to be the only "military" the Federation has, there is zero proof Federation members have their own militaries.
There may not be any "proof" (i.e. canon), but it's always made sense to me. Some worlds would depend entirely on Starfleet for defense, perhaps integrating whatever military force they
did have into a specialized part of Starfleet tasked with the defense of that specific world (see: Bajor). But for some of the members that were larger galactic powers in and of themselves prior to joining, I think they would maintain their own standing force, that might work
with Starfleet at times, but wouldn't actually be part of it, per se.
Not that such a thing would really make a huge difference in a war against the Klingons, just an interesting aside.
Again with this idle speculation?! I'm sure that would have been mentioned in the episode.
Expanding on what I mentioned in an earlier post: I acknowledge that YE is pretty clear on this topic, and that any "explanations" are speculation. However, it is true that there is nothing in the ep that precludes extraordinary circumstances, either. Now, do I think the creators had any in mind? No. Do I think they meant to show that the Klingons were capable of ultimately overwhelming the Feds? Yes.
My problem comes from the fact that I don't think the body of evidence
outside of YE supports this. If you remove YE, I think it supports a UFP victory. Thus, it becomes a contradiction, hence a desire to explain it away. For my part, given the time frame of the war (and assuming that everything leading up TO the Ent-C disappearing is exactly the same in both timelines), my explanation is based on the same one that allows the Cardassians to fight a war with the Feds over more than a decade, despite the obvious technological superiority of the latter. Rather than make this post even longer, I'll just link to a post I just made detailing this all out,
here. The same phenomenon could have occurred here, with the Klingons catching the UFP off-guard and in the middle of a "military tech slump"; the difference being that fighting from such a disadvantageous position would be FAR worse for the UFP with the Klingons, rather than the Cardassians, as opponents, thus Starfleet never really recovered, and the results are seen in YE.
So essentially, to the question "who wins?", I guess my answer IS "the Klingons", if the war started in the 2340's-2350's. Prior to that, it's hard to say. After that (2360's+), I say the Feds have the edge.
I like how your long view takes into account TUC. 
