In recent story, there have been many rifles that were considered so effective in combat, they earned the title of "winning a certain war". Examples of those are the Winchester rifle in the mid-19th century, or the M1 Garand in WWII.
It's hard to ascribe technical factors like firearms such an outsize amount of agency that their use - instead of some alternative - can reasonably be described as "war-winning". The Garand, for example: it was a good weapon, but was it so much better than everything else that it accounted for a large proportion of American military success? I think it's pretty hard to argue that. The Garand was more a symptom of the excellent American economy, industrial production, and research capabilities (a much more relevant cause for America's role in the Allied victory) than a cause in and of itself. As for the Winchester, it wasn't particularly associated with an individual war at all.
If there is any single weapon that can probably be described as "war-winning", it is the Dreyse M1841 light percussion firearm, the breech-loading rifle employed by Prussian troops during the Seven Weeks' War of 1866. The Dreyse "needle gun" was a shorter-range weapon than the main infantry shoulder arm employed by Prussia's opponents in the Austrian army, but unlike the Austrian muzzle-loading rifles the needle gun was a breech-loader. With the rapid reloading that the breech-loader made possible, Prussian infantry could maintain a hitherto unheard-of volume of fire on the defensive; on offense, Prussian soldiers fired from the hip and shot their way into enemy positions.
Normally, it's really hard for a single technical advantage to be so overwhelming that it plays a major role in deciding a war. But Prussia and Austria were very evenly matched at the strategic level. Most observers believed that neither power had a clear advantage over the other. It was in tactical situations that the Prussians really shone, and that was because of the needle gun.
Austrian infantry tactics made their forces the perfect obliging enemy for needle gun-armed troops, too. The Habsburg Empire's army was a long-service professional force that recruited from an Eastern European peasantry that was relatively unschooled and which spoke several different languages. In order to make best use of this, a simpler form of attack had to be found: rather than complex unit control and rifle marksmanship, the Austrians focused on training their troops in shock actions. It was easier to issue orders to the polyglot peasant soldiers that way, and the long period of their service could be spent on training them for the immense psychological strain of bayonet assaults in a way that conscripts could not match. Artillery would soften the enemy up, and then the army would attack brigade by brigade, delivering bayonet charges that would go in like sledgehammers. This was probably as good a solution to Austria's military problems as any; after losing to the French army in 1859 in Italy due to a overreliance on marksmanship and a failure to recognize the viability of shock action, the Austrians won the laurels of the Danish war in 1864 with their new shock tactics. But a shock charge delivered against formed Prussian infantry with needle guns in their hands was a recipe for disaster.
The war essentially came down to one battle, at Königgrätz on 3 July 1866. Time and again, Prussian forces turned back headlong Austrian charges. Green commanders used the needle gun as a facilitator: it could cover up for mistakes and help the reserve captains and lieutenants that formed the backbone of the Prussian army to learn from experience. In the Swiepwald forest, a single unsupported Prussian division, the 7th, threw back two entire Austrian corps in fighting as rough as in the Gettysburg peach orchard. In the villages of Chlum and Rosberitz, a division of Prussian Guard shattered another Austrian corps at heavy cost before being relieved by the Prussian I Corps. Eventually the Austrian army, having exhausted its strength in failed attacks against the Prussian forces, was forced to retreat, opening the way to Vienna. Victory, for the Prussians at Königgrätz, turned in large part on the needle gun; victory in the war turned on the Battle of Königgrätz.
Compared to the needle gun, it's extremely difficult to imagine a single small arm playing a decisive role in the Reaper War. Council forces were not uniformly armed; probably, no single weapon made up a high enough proportion of the whole to be responsible for much of
anything. None of the individual weapons were so much better than their alternatives to be attributed with the sort of value-over-replacement-firearm (VORF?) to mean anything. And the cause of victory over the Reapers did not lie in Council infantry's technical superiority in small arms, but in the employment of the Crucible.
But say we relax the requirement for "war-winning" to simply mean a really good firearm employed by the winning side in a war. Well, the WWII equivalent to the Harrier would probably be not the Garand, but rather something like the M3 "grease gun" - a high-quality weapon, an upgrade for an already good existing gun, that was employed by very few participants in the conflict. Would you call the grease gun a "war winner"? I doubt it.
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For further reading on the Seven Weeks' War and the needle gun, I strongly recommend Dennis Showalter's two books
Railroads and Rifles and
The Wars of German Unification; Geoffrey Wawro's
The Austro-Prussian War; Gordon Craig's
The Battle of Königgrätz; and Arden Bucholz's
Moltke and the German Wars. In German, Dierk Walter's
Preussische Heeresreformen was an instant classic when it came out eleven years ago and is still excellent today.