Being agree with what has been said, I would rise three questions about the outcome:
1. Who is going to win;
2. What awaits the Ring;
3. What impact the battle can make on Middle Earth and its people.
Regarding a possible one-to-one encounter, Tolkien says in the letter quoted above,
We have two embodied Mayar, very powerful but both seriously handicaped. Sauron's body was lost and regained several times, he wastes a lot of his power on keeping his armies together and half of his self is detached with the Ring. Still, as I can remember Silmarillion, he used to be the most powerful of all Mayar. The same book says that some Mayar were close to Vallar in their powers. Remember Gandalf's own words at Council of Elrond that Sauron is able to torture hills; shaping landscapes was Vallar's primary activity. On the other hand, Gandalf is the Spirit of Wisdom, he is close to Manve, he also has an experience of fight, including his battle with the Balrog; moreover, as Gandalf the White he is seriously enhanced, and wears the Ring of Fire. I tend to believe, that of the four elements, air and water would surve to Gandalf (influence of Vallars and the Three) while earth is going to be subjugated to Sauron. Fight for Control over fire is going to be the main issue of the battle. The most probable outcome, as it seems to me now, will be the same as in case of the Balrog: both die in the battle.
Another issue is that no-one expect Sauron to be ownest. Should Gandalf come to Mordor and require satisfaction, Sauron would've act like Witch King dealt with the last king of Gondor. Another option is the battle of Moranon Gates when both armies were present, and, possibly, completely destroyed by the fury of two Maiar.
So if Sauron wins, the result is evedent. Otherwise there can be several options, connected to two other questions. Contradicting to himself, Tolkien says in the quoted letter that
Quote:
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If Gandalf proved the victor, the result would have been for Sauron the same as the destruction of the Ring; for him it would have been destroyed, taken from him for ever. But the Ring and all its works would have endured. It would have been the master in the end.
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Probably, a Maya can kill Sauron without undoing the Ring but then it would be very difficult to undo it. In abscence of the threat people of Middle Earth are unlikely to see the reason why the Ring should be undone. Even elves can resist the idea as the Three can endure there magic only with the One around. So should Gandalf survive the battle or not, the Ring is likely to win and a new Dark Lord would emerge (singular or collective).
Finally, such a combat can have devastating impact on Middle Earth.