It's already well-established that Qui-Gon was incredibly strong with the Force. He continuously studied the ways of the Force and eventually learned enough about the Cosmic Force and the Living Force to unlock the secrets of eternal life.
We are just barely seeing a 600-something-year-old Yoda in the High Republic era. And given that Qui-Gon Jinn dies in 32 BBY, a fight beyond that point would be pointless since, as a Jedi spirit, Jinn would arguably be stronger than the still physically alive Yoda.
Though he consistently disagreed with and defied the Jedi Order, Qui-Gon understood the Force better than any other Jedi Master, truly believing in the good it could cause. A powerful fighter for peace and understanding, Qui-Gon Jinn was the greatest Jedi in all of Star Wars.
Very powerful. He was an excellent duelist; one of the best duelists at the Order. He was very intelligent and insightfull.
Obi Wan in his prime (ROTS) was more powerful than Qui Gon. Qui Gon was getting stomped by Maul I'm Tatooine and was exhausted at the end of their duel. In AOTC Qui Gon was implied as superior to AOTC Kenobi by Count Dooku.
Qui-Gon was ultimately defeated by a move that can only be done with a double-bladed lightsaber as Darth Maul used the handle of the weapon, striking Qui-Gon physically on the chin, stunning him for just long enough to deliver the killing blow.
Originally Answered: Why was Palpatine afraid of Qui Gon Jinn? I believe Palpatine was truly afraid of only 2 people. They were those who could threaten his plans. He knew how powerful he was, but he was also afraid of failure, he wanted power and once he got it, he wanted even more.
While little is known about Yoda's species, we do know, however, that their entire race is incredibly gifted in the force. Both Jedi Master Yaddle, and now Grogu hold great force powers, but no Jedi Master has ever held greater power than Jedi Master Yoda.
Though Qui-Gon Jinn was strong in the ways of the Force, including telepathy and levitation, there's just no way he would beat Luke Skywalker in a fight. In both of their primes, Luke still makes for a better swordfighter with better agility. Qui-Gon isn't known for being a strong fighter.
The reason why Qui-Gon Jinn is the most powerful Jedi in the galaxy is because he had seen everything that would unfold throughout the Skywalker Saga in a vision of the future, sacrificing himself to ensure the fulfilling of the Chosen One prophecy.
The Shaman of the Whills and Five Priestesses
Even though he perished in battle, Qui-Gon Jinn's consciousness continued. He had found the secret to immortality through the Force.
The latest Star Wars tie-in novel confirms Qui-Gon Jinn was the one Jedi who could have stopped Palpatine and even saw his plans in action. Star Wars has confirmed Qui-Gon Jinn was the one Jedi who could have thwarted Palpatine's plans.
Palpatine admits to Darth Vader that the Jedi he actually feared most was none other than Jocasta Nu.
Mace Windu failed in his mission to arrest Palpatine in Star Wars: Episode III - Revenge of the Sith, but Yoda may well have fared better. As powerful as Darth Sidious may have been, it's easy to forget he actually seemed afraid of Master Yoda.
Arguably, some of the rarest types of Jedi were the so-called Iron Knights. These are members of the Shards species - crystals with a brain of their own.
But one Jedi stands above the rest and needs to start getting recognized as the greatest Jedi who ever lived. That is none other than Obi-Wan Kenobi. While this saga is ultimately the story of the Skywalkers, Obi-Wan is arguably the best and most pure Jedi to ever come out of it.
Obi-Wan discovers that Qui-Gon's old master, Count Dooku, has become a Sith Lord; and Dooku mentions Qui-Gon as he interrogates a captured Obi-Wan, expressing grief over his former apprentice's death and debating that Qui-Gon would have followed him in leaving the Republic had he survived.
There, he discovered Anakin Skywalker, a boy with enormous strength in the Force. Qui-Gon believed Anakin was the Chosen One, prophesied to bring balance to the Force, and that their meeting was no accident.
When Qui-Gon Jinn showed up on Naboo and threatened to throw a bantha-sized wrench into his plot, Palpatine had to act fast. He dispatched Darth Maul to get rid of the Jedi Master once and for all. Therefore, just like Yoda said, Palpatine's fear led to evil deeds, death and the rise of the dark side.
Padawan Windu was trained in the ways of the Force by Jedi Master Cyslin Myr.
The Jedi understood "the balance of the Force" to refer to the absolute defeat of the dark side, but Qui-Gon believed darkness and light were both necessary for balance. Anakin would have grown to understand his destiny far better had he been trained by Qui-Gon instead of by the Jedi.