Harry Potter's Wand Research Paper

Harry Potter Who has the most powerful wand? (Between Harry Potter, Albus Dumbledore and He-Who-Must-Not-Be-Named)

WARNING: SPOILERS TO BOOK 6 AND 7 (This is based on the books, not the movies)
To start off, let me just say that I’m talking about who had the most powerful wand during the course of 6th to 7th year. Or, in other words, The Half-Blood Prince and The Deathly Hallows.

First of all, let's talk wands, wand cores and wand woods.
Harry’s Wand, is Holly and Phoenix feather, eleven inches, nice and supple, and shares it's core with Voldemort's wand, before he got the Elder Wand.
Dumbledore’s wand, Elder and Thestral tail hair, 15 inches. Yes,

As you can probably tell, Voldemort’s and Harry’s wand both have a phoenix feather core, meaning they are Twin Wands. A Twin Wand, by the way, are two wands with the same core.

Phoenix wand cores are the rarest types of cores. Phoenix feathers are capable of the greatest range of magic, though they may take longer than either unicorn or dragon cores to reveal this.
So, both Tom and Harry have quite the rare wand.
But what about the Elder Wand? It has a Thestral Tail Core. Ollivander didn't choose to work with such cores, but Thestrals have a strong connection with death, plus the magical properties of invisibility, flight and a strange ability to find their destination. How this affects the wand is uncertain, but it does show that there's some seriously powerful

It works best for people who may need help overcoming anger or carelessness (looking at you, Harry). Holly wands also choose owners who are on a dangerous or spiritual quest. Holly is one of those woods that changes most in performance depending on the wand core, and it is a very hard wood to teamup with a phoenix feather core, as the wood's dangerous nature prices conflicts strangely with the phoenix's lack of interest. In the unusual event of the two cooperating, nothing and nobody should stand in their way.
Voldemorts wand wood is Yew, a rare kind of wood just like Holly. Their usual partner are usually unusual, or infamous. Yew wands have a dark and scary reputation in duelling and curses. Fits Voldemort quite well, doesnt it? However, it is unfair to say that those who use yew wands are more likely to be attracted to the Dark Arts, it depends on the person.
Dumbledores, or the Elder Wands wood is, of course, Elder. The rarest wand wood of all, and known to be extremely unlucky. The old superstition, ‘wand of elder, never prosper,’ has its basis in this fear of the wand, but in fact, the superstition is baseless, and those foolish wandmakers who refuse to work with elder do so more because they dont think they will be able to sell their products than from fear of working with this wood. The truth is that only a highly unusual person will find their perfect match in elder, and it's a very rare occasion