Short answer: "It depends". The main things it depends on are:
- Can Dumbledore bring himself to use Avada Kedavra?
- Does Gandalf's light shield thingy repel Avada Kedavra? It stopped the freaking Balrog, but AK is claimed to be unstoppable... so maybe, maybe not. Unstoppable force, meet immovable object.
- Assuming AK can break the light shield thingy, can Gandalf find some other way of nullifying it? It can't be magically blocked, but as the movies have shown at length, you can just dodge it, or make sure there is some other cover in-between. I would give Gandalf better odds in the forest or swamp if there is cover to hide behind. He could also just be quicker "on the draw" and throw Dumbledore around, pull the wand out of his hand, or otherwise disable his casting hand.
- Likewise, does "Protego" do anything against Gandalf's powers? Given it explicitly doesn't work against AK its fair to say Gandalf would have something that would get through.
Ultimately we can probably conclude this would be a very quick fight, as neither of them can reliably stop the other's powers.
So, assuming Dumbledore doesn't open with Avada Kedavra and assuming Gandalf doesn't use the light shield thingy, I'd have to go with whoever is first to react. Both of them can pull the wand/staff out of the other's hand, and both are fairly useless without their casting implement of choice. If they both did it at the same time and disarmed each other it would come down to their respective skill with a sword, which I would have to give to Gandalf who has at least been seen using one. Dumbledore definitely has the better sword (is Glamdring even magical?), but we've seen no evidence that he has any skill with it.
So... I'm going with Gandalf I guess. How many nerd points do I get for this post?