I don't really know much about Gandalf, except the movies, and I read all the Harry Potter books, so I don't know how accurate I can be with this.
but from what I've seen, I don't think Gandalf stands a chance. Dumbledore has apparition, to teleport instantly, and silently, something few wizards can do.
The Elder Wand does not make you win any battle, it's just an extremely powerful wand. Dumbledore vs Grindelwald(who was already the most powerful dark wizard at the time) meant that, even though the Dark Wizard had the most powerful wand in the world, Dumbledore was still a shade more better than him. Combine his already powerful abilities with the Elder Wand is just... i don't know, big big...
Gandalf is strong, but I noticed that he doesn't use his magic often in the movies. Either because of plot, or because if he does, he has to wait a while for his power to recharge, I don't know. I hope someone can explain this please.
Dumbledore can transfigure objects, manipulate elements, make himself invisible, and cast spells in an instant, without uttering them out loud.
Combine that with his already impressive dueling skills and extremely high intelligence, I don't think Gandalf stands a chance.
But I only know Movie Gandalf. And if he needs to chant to use magic, he won't last long. The wizards in Harry Potter fought so fast that their arm movements were a blur, shooting spells instantly at one another like swordsplay.
Gandalf hasn't displayed a lot of quick powerful spell works that I've seen.
But again, I haven't been able to read much of the LOTR books to see how powerful he can truly be. I read here he's a Divine being, but I have no idea if that helps him in anyway in combat. Does it give him access to more powerful spells, transforms him into an angel or something else?