In close-quarters combat, Gandalf easily has an upper hand because of the weapon he wields. Glamdring, the Elven blade he uses, would put Dumbledore in a spot of trouble. He'd need to maintain his distance at almost all times during this battle, while Gandalf would be comfortable fighting at both short and long ranges.
Gandalf is greater than Dumbledore, although (or perhaps because) he had less power. He rallied all the free peoples of Middle-Earth to the cause, gave them heart, and sacrificed himself to save his friends and the quest in Moria. He worked tirelessly for centuries.
Gandalf is Immortal
However, as we know from the books and movies, Dumbledore is far from immortal. At the end of the day, Albus Dumbledore is just human being with magical gifts. Gandalf is an immortal spirit like an angel with almost limitless potential power. Gandalf “dies” and comes back stronger.
Gandalf. He's a maia, an agent of the Gods on Middle-Earth, and as such he's immensely powerful, but never uses his full strength because the people of middle-earth must make their own destiny, maia should not interfere. However, in a no holds barred fight against yoda, he would simply unleash his divine might.
Hermione could beat Dumbledore any day if she wanted to. She's one of the most brilliant minds of her generation; like any good Gryffindor, she's brave, loyal, and strong. She mastered advanced spells at a young age, could make any potion perfectly, and her quick thinking saved her, Ron, and Harry more than once.
Albus Percival Wulfric Brian Dumbledore was the only wizard Voldemort ever feared and the only one who could have defeated him in a duel. Albus Dumbledore is the most powerful wizard in the Harry Potter.
During book 7 is definitely Voldemort. By the time of the Cursed Child, it's probably Delphini. As for your other questions: Dumbledore was not powerful because of the Elder Wand. He took it from Grindelwald after defeating him in a duel (with a regular wand).
More cunning and devious than all but the most attuned Force-sensitive beings, Darth Bane could more than likely defeat Yoda in a battle of both strength and wit.
One of the main reasons why Yoda would've won against Anakin is simply because he was far better trained than him. Yoda could see the moves his opponents were going to make before they made them; therefore, battling against Anakin would've put him at a far heavier advantage.
Most of the time that Gandalf knows Saurman he is known as Saruman the White. He was originally the chief of the wizards as well as the White Council that was formed to fight against Sauron. He was more powerful than Gandalf at these stages, but his study of dark magic turned him to support Sauron.
Gandalf without a doubt. As mentioned in Silmarillion Gandalf is wisest of the Maia. This means he was actually wiser that Saruman the White.
Yet, despite his magnificent abilities, Gandalf is still low on the totem pole of powerful beings in Tolkien's lore. This might be surprising to a lot of characters, as he's often regarded as one of the strongest people in that universe.
From the depiction of the scene in Peter Jackson's film adaptations, it seems very clear that the Witch King has the upper hand of the battle, and that he is able to muster more power at that moment than Gandalf is.
Gandalf absolutely could have killed Smaug in a one-on-one fight. The grey wizard fought and defeated the Balrog of Moria, and a dragon was a lesser evil than that.
Strong: Albus Dumbledore
Most regarded him as the strongest wizard in history, and even Lord Voldemort himself feared to face him. Beyond his many impressive titles and positions of power, Dumbledore exhibited absolutely extraordinary abilities on several occasions.
#1 – Yoda. Yoda is widely considered to be the greatest Jedi of all time, and with good reason. He is a master of the Force, a skilled warrior, and has an unmatched wisdom that comes from centuries of experience. He is the embodiment of what it means to be a Jedi, and his legacy lives on long after his death.
Master Yoda has risen above all others to claim the top spot as the most powerful Jedi of all time and the true chosen one according to IGN's audience. He won pretty handily as well, as he was victorious in 89,756 of his 95,243 battles and had a win percentage of 94.2%.
If we're to come to a definitive decision on who the strongest Jedi ever is then we have to consider more than their physical skills and strength. Master Windu could be the strongest Jedi ever, he's strong, trained, wise and proved his abilities in combat as well on the Jedi council.
As powerful as Darth Sidious may have been, it's easy to forget he actually seemed afraid of Master Yoda. As seen in Revenge of the Sith, Palpatine initially thought he could deal with the aged Jedi Master - and then, when Yoda proved able to counter the Sith Lord's Force lightning, he fled.
Aside from agility and telekinesis, Yoda could absorb and redirect Force attacks, like lightning. Because of his higher understanding, he would easily overcome Darth Vader in a fight, though that doesn't mean it wouldn't be a difficult battle.
Sidious is also known as The Emperor of the Galactic Empire. He rose to power in the Senate as a Senator from Naboo and lived a double life as a Sith Lord. Sidious is extremely powerful and held very complex knowledge of techniques to master the dark side's force energy.
Minerva had mastered the Patronus Charm, being able to create a powerful corporeal Patronus in the form of a cat — identical to her Animagus — , being the only person seen to cast three Patronuses at once. She also was able to use her Patronus as a means of communication, as taught to her by Dumbledore.
Voldemort intentionally made six Horcruxes, but when he used Avada Kedavra on Harry, he unintentionally created a seventh Horcrux. Instead of dying, Lily's love for Harry created a counter 'curse' known as Sacrificial Protection and saved Harry.
For example, in Harry Potter and the Deathly Hallows – Part 2, Snape was reluctant to fight McGonagall when the latter took him to a duel in front of Hogwarts students. Both characters had their strengths, but the last Harry Potter movie proved Snape was the strongest Hogwarts professor.