Both wizards are at the peak of their power. This means that Gandalf is now Gandalf the White. He has his staff and Glamdring. Dumbledore has the Elder Wand. They are in the courtyard at Hogwarts. They are 20 feet apart. All out duel, no one holding back.
Dumbledore has a much wider array of magical abilities and in raw power is no slouch, at least when compared with what Olorin was allowed to show while in mortal form.
The thing, however, is that Gandalf is way quicker than his appeareance would suggest and can do a number of things to cripple Dumbledore (breaking his wand or making it burn, for example) that could give him the win.
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Gandalf's magical power is great enough to crumble the sides of mountains, and he did this as Gandalf the Grey. Beyond that, his speed is explicitly superhuman, his movements being difficult for even peak humans (Maybe even slightly superhuman) like Aragorn to accurately perceive.
He wins pretty handily.
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"I don't fight for good, and I don't fight for evil. I just fight!"