That's like saying Voldemort could only beat Harry with his phoenix wand and would lose if wandless. Just because Dumbledore's wand is stronger than most doesn't mean it shouldn't be counted as part of his powerset.
I disagree. While wands aren't all created equal none of them make their user undefeatable or damn well near it...
Simply put the Elder Wand>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>any other wand.
If we're talking Harry Potter wizards... Their wands are a way to control and focaus their magic. Some very powerful wizards (Voldy/Dumbledore) can do controled wandless magic.
"The wand chooses the wizard"
We are left to take this the way we want. Wand magic/law is still a huge mystery. But in the story they do tell us that "in combat" Elder Wand<Any other wand. Only if the Elder Wand has alligence to the wizard.
Also what the story tells us is that it's the wand and wizards connection that makes it most powerful. EX.. when Harry's wand gets broken and has to use the stolen wand or hermione's wand. It doesn't work well because there is no connection between him and those other wands.
My fault its in OOTP. Dumbeldore says, "I knew tat Voldemort's knowledge of magic is perhaps more extensive than any wizard alive. I knew that even my most complex and protective spells and charms were unlikely to be invincible if he ever returned to power."
Well, I still don't know if Voldemort is better than Dumbledore. Dumbledore was winning with the elder wand, but without it.. If you read the book it was clear that Dumbledore had an advantage through most of the fight. My top 10 is
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2. The Perceival Brother who chose the Invisibility Cloak.
3. The Brother who chose the Elder Wand.
4. The Brother who chose the Ring.
5. Dumbledore [Dumbles has all the powers both Grindlewald and Voldemort have/had, but chooses not to use them.]
6. Grindlewald [after all, Dumbles beat him]
7 Harry Potter [is powers are mostly potential in the books, even up to DH, but dood, he is destined for great things.
8. Voldemort. Uber-powerful, but failed to kill Harry each time he tried.
9. Severus Snape. Enough magic to make sure Voldie doesn't find out that he's a double... triple? - crosser. That's pure, concentrated, POWA.
10. Bellatrix Lestrange/Sirius Black. The first wouldn't be Volde's ho if her power levels weren't so high. The second hiding in plain sight in Hogsmeade during the invisible rise of Voldemort in OotP.
It does not do to dwell on dreams and forget to live.