So in the first 5 or 6 books, it was very clear that the wand chooses the wizard and the power/level of the spells the wizard produces is based on the knowledge and skill of the wizard. This is referenced by people constantly being telling Harry that he wasn't skilled enough to perform certain spells, or Bellatrix telling Harry that he needed to mean the Cruciatus curse for it to be effective. However, in the 7th book, this entire idea is changed to the wand being the thing that's powerful and regardless of the wizard's/witch's skill or knowledge, he/she could still perform a very advanced spell if it's something the wand could handle. Goyle accidentally creating a fire serpent is something that instantly comes to mind from the movies(I don't remember if that happened in the book). So, my question is, what actually holds the power, the wizard/witch, or the wand?
There is a quote written by J.K Rowling, and it states,
“Wands are only as powerful as the wizards who use them. Some wizards just like to boast that theirs are bigger and better than other people's.”
The quote can be found Here.
I do believe that the reason Harry could not cast "Crucio" was an exception due to the reason that Harry was not fond of the Unforgivable Curses. Harry had not cast crucio (to my knowledge) before, so he did not understand what the requirements were for the spell.
Wizards learn magic as the years progress at Hogwarts. There were classes in the books that were not shown due to the amount of wasteful space it would cause. In these classes, other spells and enchantments were taught, so the reader did not physically see them. So it is most likely that, "a very advanced spell", was already taught. The fact that Goyle "accidentally" creating a fire serpent, may not be accidentally.
A statement on Harry Potter Wiki states: "The Carrows were also there at the school, with Amycus Carrow teaching Defence Against the Dark Arts, though in reality he taught the Dark Arts. There were many favoured students, such as Vincent Crabbe and Gregory Goyle, who were encouraged to practice the Cruciatus Curse on rule-breakers."
During the time that the Carrows were teaching favoured students, they most likely taught other Dark Arts, and the fire serpent was probably one of them.
The wizard/witch is the one who is powerful, not the wand. Again, the quote backs this statement up.
Find the quote Here.
The answer is really both.
The relationship between wand, wizard, and spell power is not a simple one. Wizards clearly have power separate from their wands, since wizarding children frequently produce magic spontaneously. On the other hand, that the use of wands increases the effectiveness of spells is obvious from the very premise.
If having a wand did not make magic easier, there would be little reason for any witch or wizard to use one. Indeed, we see strong evidence that a wand is not only helpful, but in fact necessary for some spells as early as Harry Potter and the Goblet of Fire:
Comprehension dawned suddenly on Bagman’s round, shiny face; he looked up at the skull, down at Winky, and then at Mr. Crouch.
“No!” he said. “Winky? Conjure the Dark Mark? She wouldn’t know how! She’d need a wand, for a start!”
The manner in which Winky is treated when she is discovered with a wand fits well with Griphook's comments several books later:
“Well, goblins can do magic without wands,” said Ron.
“That is immaterial! Wizards refuse to share the secrets of wandlore with other magical beings, they deny us the possibility of extending our powers!”
There is much stronger evidence, though, from Harry Potter and the Philosopher's Stone! This comes to us from the acclaimed wandmaker, Garrick Ollivander himself:
"I'm sorry to say I sold the wand that did it," he [Ollivander] said softly. "Thirteen-and-a-half inches. Yew. Powerful wand, very powerful [emphasis mine], and in the wrong hands... well, if I'd known what that wand was going out into the world to do...."
Or perhaps this:
"Ah yes," said the man. "Yes, yes. I thought I'd be seeing you soon. Harry Potter." It wasn't a question. "You have your mother's eyes. It seems only yesterday she was in here herself, buying her first wand. Ten and a quarter inches long, swishy, made of willow. Nice wand for charm work [emphasis mine]."
Here, in the very first book in the series, a wand is described as powerful, or as good for charm work. So from the very start of the series, the very book that gave us the quote "the wand chooses the wizard," it is clear that wands have intrinsic powers, quite apart from whichever wizard wields them. That the wand chooses the wizard certainly means that not every wizard will be able to take advantage of them, however.
Viewed in this context, the Elder Wand is not an exception to the previously established rules of wandlore. It is much more powerful than any other wand, but that is a matter of degree, not kind. What makes the Elder Wand special is actually its personality. Per J.K. Rowling:
The Elder Wand is simply the most dispassionate and ruthless of wands in that it will only take into consideration strength. So one would expect a certain amount of loyalty from one's wand. So even if you were disarmed while carrying it, even if you lost a fight while carrying it, it has developed an affinity with you that it will not give up easily. If, however, a wand is won, properly won in an adult duel, then a wand may switch allegiance, and it will certainly work better even if it hasn't fully switched allegiance for the person who won it. [...] However, the Elder Wand knows no loyalty except to strength. So it's completely unsentimental. It will only go where the power is. So if you win, then you've won the wand. So you don't need to kill with it. But, as is pointed out in the books, not least by Dumbledore because it is a wand of such immense power, almost inevitably, it attracts wizards who are prepared to kill and who will kill. And also it attracts wizards like Voldemort who confuse being prepared to murder with strength.
To address the question of Fiendfyre, I am not aware of any particular evidence that Voldemort could not cast Fiendfyre. The reason he did not may well have been its indiscriminate destructive tendencies toward ally, enemy, and caster alike.
The Wizard holds the power, but the wand helps channel it
Wands channel magic so as to make its effects both more precise and more powerful, although it is generally held to be a mark of the very greatest witches and wizards that they have also been able to produce wandless magic of a very high quality. As the Native American Animagi and potion-makers demonstrated, wandless magic can attain great complexity, but Charms and Transfiguration are very difficult without one.
(Pottermore - History of Magic in North America)
In GOF Barty Crouch Jr. disguised as Mad eye mentions about the Avada Kedavra:
Avada Kedavra’s a curse that needs a powerful bit of magic behind it — you could all get your wands out now and point them at me and say the words, and I doubt I’d get so much as a nosebleed.
So I guess you need to have a certain level of magic even if you know the incantation and have a good wand to be able to do actual damage. The above mentioned along with the fact that you need to mean the spells (like crucio) for them to actually work points to the fact that you do need a powerful wizard to be able to do advanced spells to their full potential.
Wands are like icing on cake I guess. But you need the cake to be good in order for the icing to add to the flavor.