Obvious answer:
Yoda forces Dumbledore’s wand away from him. A wandless wizard is powerless and a Force swipe cannot be prevented with regular magic because it’s not a spell. Yoda then does as he pleases with Dumbledore’s soon-to-be-cadaver.
Obvious counter:
Dumbledore forces Yoda’s lightsaber away from him (Expellio!). Then turns him into Grover. Yoda’s tricks without a lightsaber are unimpressive to any Potter wizard, but especially one of Dumbledore’s caliber.
Or he just uses Avadra Kedavra, which is way dark for Dumbledore, but there’s no counter or block for it.
I’d also be very cautious saying Dumbledore is powerless without his wand. The guy’s got tricks.
I’ll also say that “knock his weapon from his hands from a distance with the force” is the kind of intelligent use a Jedi never puts his powers to.
Whereas “take the wand” is elementary duelling for a wizard. Even if Dumbledore’s having an off day, he’d know to take the lightsaber.
I gotta go with Dumbledore. Yoda has some nifty tricks, but nothing beyond telepathy and telekineses. Dumbledores wizardry qualifies as reality altering. Yoda ain’t gonna flip his way out of that one.
Or Fozzy Bear. Maybe he already did. That would explain a lot.
Let’s make this general and break this down, shall we? Only the movies (for SW) or novels (for HP) need apply.
Jedi/Sith vs. Wizard:
Powers:
Jedi: Enhanced reflexes and agility, superhuman running speed and leaping, telekinesis, limited precognition, “force lightning”, empathy, precognition, and the “Jedi mind trick” (limited by the target’s species and perhaps will). Effects increasing longevity and resurrecting the dead are hinted at, but never directly shown.
Wizard: Too many effects to list, but including tranforming objects (including self and opponent), telekinesis, mind control and telepathy, healing (wizards have superhuman longevity) and various charms and curses that range from annoying and disorientating (the Bat-Bogey Hex) to the incredibly deadly (Avadra Kedavra). Resurrecting the dead is the only thing said to be truly impossible, but even then there’s ways around one’s own mortality. True divinition exists but is rare.
Advantage: Wizard, but not by much. Wizard’s have a much wider variety of spells to choose from, but the Jedi’s powers are optimized for combat.
Weapons and Tools:
Jedi: Lightsabres. The Star Wars universe also has advanced technology including blasters, droids, and starships. Jedi or their allies can be from many alien races, some of which have superhuman capabilities.
Wizard: Magic wands are key to a wizard’s use of magic. A wizard can be effectively disarmed by removing him from his wand, but some powers can still be activated. Wizards also have access to potions (which can replicate most spell effects and then some, such as the powerful luck potion Felix Felicitans), magical objects, and magic creatures such as dragons.
Advantage: Tie. We all know this will come down to wands and lightsabres anyway. Although Felix Felicitans means the drinker wins (or if he loses, he’ll end up better off than if he had won somehow anyway), so we’ll just assume that’s not part of the picture, and a dragon versus X-Wing fight would be pretty damn cool.
Ranged Tactics: Jedi: Close range. If not possible, toss a heavy object with telkinesis or use force lightning.
Wizard: Virtually all wizard spells are ranged. Wizards, while not tehd edicated warriors that Jedi are, have a semi-formalized practice of dueling. Tactics vary, but usually the wizard will attempt to disarm, disable, or kill his opponent with a single well-placed spell. Spells can sometimes be dodged, but some, like Avadra Kedavra, cannot. Wizards can also create personal shields (Protego) that block spells. It’s hard to say how they’d interact with Jedi powers or lightsabres, but I’d guess they’d be effective. The Force is close enough to magic.
Advantage: Wizard. Jedi are fast, but are they fast enough to close range before they get knocked off their feet by a hex? Wizards fight smarter at range anyway, using a huge variety of tools to fit the situation.
Melee Tactics:
Jedi: A flurry of lightsabre blows and parries.
Wizards: Wizards don’t get close unless the fight has degenerated to brawling.
Advantage: Jedi. If the jedi can get to lightsabering range before being stunned or diasrmed, the wizard is toast.
Overall: Your rookie Jedi will beat your rookie wizard. The Jedi are fast and dedicated fighters. Once you get to the level of Dumbledore or Voldemort, however, even the most experienced Jedi will fall before their varied and powerful ranged attacks. Even a quick and courageous Hogwarts student (like Harry) could take out Palpatine if he had some warning.
Um, they’re both on the “Light Side” and would never fight one another. And Dumbledore would never use Unforgivable Curses. They go have a nice drink together and figure out how to defeat Voldemort and the Sith.
Given how very rarely they use, I’ve come to the conclusion that they can’t - at least, not casually and easily. Nothing else just makes sense. Sure, maybe the Jedi wouldn’t. But I have a hard time seeing the Sith avoid it as often as they do.
The times we’ve seen them use it, it was usually a finishing move to clear away a beaten opponent (Dooku in Ep 2 & 3), or something they planned, concentrated on, and focused heavily (Obi-Wan in Ep 1).
We all would win, Caricci, we all would win.
Where are you getting the info in which the Avadra Kedavra is undodgable? Wasn’t Harry dodging them from behind the statue in the Ministry of Magic in HP:OOTP?
Also, I’m not sure why you’re implying that the Protego spells would have any effect on lightsabers. They seem to only block jinxes and curses, not physical objects. A lightsaber for sure, and probably force lightning would plow through any defensive spells.
I think you’re underestimating the Jedi precognition too. With focus they’d never be caught off guard by anything the wizard might throw at them.
Light sabers can’t cut through the “blade” of another light saber, but they can cut through the handle.
Were those AK’s, or other spells? If you could simply dodge them, then it seems like they were making a really big deal about them in GoF.
Do they? Harry knocks Snape on his ass with one in HBP, so they’ve got some physical effect. In any event, a wizard could build an energy field that was impentetrable to a lightsaber (the magical equivalent to a force field), they just don’t have any reason to in the Potterverse.
Jedi precognition SUCKS. It gives some prior warning, but not bloody much. Or else they wouldn’t have been all but eliminated by clone troopers shooting them in the back.
Well, it depends if you go by the getting shot in the back scenes, or the blocking blasters blind and shooting torpedos into vent shafts. Not exactly consistent. Also, remember what happened when they tried that on Yoda? I’d say his precognition is pretty formidable.
Just checked OotP and Voldy fires a AK at Harry and Dumbledore animates the fountain statue which jumps in front of the spell causing it to deflect at the last second.
This seems like evidence that it, like most all other spells, can be avoided and deflected with simple solid objects. A lightsaber would deflect one as well as anything else.
Mexican standoff. They’re both strong on defense and neither are particularly strong on offense.
Fair enough. Then Dumbledore just has to cast Expellio first, then the Bat Bogey Hex (or whatever).
I’d say Yoda’s foresight is probably enough to keep Dumbledore from getting the drop on him, but D’s got more than enough to take him in a stand-up fight. Mere Jedi knights would be getting punked by third year Hufflepuffs, though. 
Unless the spell was to transform the lightsaber itself… into a wet noodle. Wouldn’t do a heck of a lot of good then.
We also have to face the fact that spells don’t always require bolts of light or anything: that’s just curses and jinxes and such. A lot of spells, including unspoken ones, just DO stuff. Dumbledore seems to be a master at this.
Accio Yoda’s lightsaber!
Again, people: MAGIC. That outstrips anything a Jedi can do. Jedi may be formidable infantry, but in the end they have their own fairly simplistic physical effect on the world, bound to particular laws of physics. Wizards can alter reality. The only Jedi that even comes close to reportedly having that sort of power is Darth Plaugius or whatever his name was.
Yeah, after a million cryptic babblings, closing their eyes, straining and sweating with their hands and SLOOOOOOWLY the rock starts to move. Very impressive.
My thoughts exactly.
Now Vader vs Voldemort in a battle. Two power hungry meglomaniacs.
Discuss.
I’ve only seen the HP movies, so I don’t have the whole picture… but does Dumbledore ever actually do anything? Every movie so far, he’s been farting around in his study while a twelve year old kid foils all the evil plots. The only Jedi dumb enough to rely on a preteen to solve things was Qui Gon, and look what happened to him.
Bottom line: if it’s one on one, Dumbledore is screwed. If there’re some nearby children he can endanger, he might have the edge on Yoda, though.
Who cares? Bring on the Yoda/Dumbledore crossover slashfic! 
“A mighty wizard Dumbledore is! But his staff compare to Yoda’s lightsaber can?”