With reference to material from the books as quoted in this question, it appears Aragorn's army gained the upper hand. Although Sauron sent the Nazgul to turn the tide, the Eagles arrived in time to keep the air battle in check. The battle ended prematurely because of the destruction of the One Ring.
Considering the current state of the battle at that point, is it possible for Aragorn's army to emerge victorious against Sauron's army if the battle is allowed to run its course (ie. if the Ring was neither destroyed at Mt Doom nor recovered by Sauron before the battle's end)?
Edit: I feel like people aren't seeing what I'm looking at. I'm referring to this passage quoted in an answer for the question I linked earlier:
Against the Host of the West was arrayed all of Sauron's hordes of orcs, Trolls, and barbarian Mannish allies such as the Easterlings and Southrons (Haradrim). An exact count is not given of the number of Sauron's forces, but it is said that they were "ten times and more than ten times" greater than the Host of the West, making it a force of at least 60,000. Sauron's forces surrounded the Armies of the West on three sides, with the Easterlings on the left flank, the Orcs held the center, and the Haradrim on the right. The Armies of the West always had cohesive stability within their center and kept the Enemy from breaking through by force of numbers. The solid infantry squares of Gondor infantry beat off their inferior Orcish opponents while the Rohirrim cavalrymen staved off the archers of the Harad. The small force of Easterlings launched a quick attack before being repulsed by the armies of Gondor and Rohirrim while the larger Haradrim force slowly retreated to the hills. By now, pressure had eased off of the flanks of the Armies of the West, who smashed into the lines of the Orc-host, slowly beating them off and forcing a retreat back through the Black Gate (though not without suffering sizable losses of their own).
If the army of Mordor, after emptying the land of his dark host, still ends up in retreat before Aragorn's advance, does it not mean that the odds of victory is actually more than negligible if the battle is permitted to play out with the Ring neither destroyed nor returned? The Army of the West is no longer outflanked, the Orcs couldn't hold the line, the Nazgul were focused on the Eagles.