The nature of the world of Avatar makes it difficult to compare one Avatar to another. Only one can exist at a time, and because the Avatar State each can enter is the culmination of all past Avatars' power and experience it's easy to assume that each Avatar is more powerful than the last. But an actual comparison between them reveals that that's not the case.
By looking at the feats each Avatar actually performs, and combining that with an analysis of their own unique skills, powers, and approach to fighting it's clear that the power in the Avatar lineage isn't some neat progression. Here are the most powerful Avatars of all time, ranked from the weakest to the strongest.
Unnamed Avatars
There are countless Avatars seen only in visions and flashbacks, and most of them do not have names or any feats attached to those names. The most notable among all the unnamed Avatars is probably Yangchen's predecessor, a Fire Nation Avatar briefly seen to erupt four volcanoes simultaneously. Lavabending was thought the be an Avatar-specific combination of firebending and earthbending until Ghazan whipped it out in The Legend of Korra, but the feat remains impressive on its own even after that.
Roku
Aang's predecessor and mentor from the Fire Nation was a towering figure when he first appeared. After taking over Aang's body during the solstice, Roku easily disposed of Zuko and his allies, melted the chains off Aang's friends without hurting them, and destroyed the building he was in as his grand finale. Further displays of his power would not be seen until The Avatar and the Fire Lord where he bent massive waves of all four elements and easily dispensed with Fire Lord Sozin himself.
Unfortunately, in the same episode, he was ultimately killed by a volcano. While his advanced age and poisoning by the volcano's fumes contributed toward his death, it makes for a lackluster showing compared to most other Avatars.
Yangchen
Although little was seen of the last Air Nomad Avatar before Aang in either series, Yangchen received a lot more focus on the comics and games. In the show, she commands a gust of wind that sweeps over a yawning field of grass, but in the comics, she goes one further and enters combat with the colossal spirit, General Old Iron. It was in that battle she revealed her ability to surround herself in the same sphere of elements Aang later uses against Ozai, and her advice to Aang to end Ozai's life makes it clear that she was a deadly and formidable force.
Wan
As the very first Avatar, one would expect that there would be a learning curve that would put Wan further down on the totem pole. He earned his mythic status for a reason, however, and his showings in the two-part episode of The Legend of Korra that explored his origins are nothing to dismiss.
In the two-parter, Wan not only advances the art of bending more than any human ever had before (learning to shape elements rather than merely blast them), but he did it while exploring a premodern world filled with monsters and conflict. It was his climactic battle with the evil spirit Vaatu where he showcased the full-force of his abilities. Not only is Vaatu far more powerful than General Old Iron, but Wan decisively beat him rather than ending with a bargain.
Kuruk
Another Avatar that receives very little attention, all that was really known about Kuruk's abilities at first was a flashback showcasing the tidal wave he both produces and surfs on. Later on, there was more revealed about his backstory, fleshing out his arrogance as he traveled the Fire Nation winning Agni Kai duels and besting the Earth Kingdom's greatest in contests of strength, but it was not until The Rise of Kyoshi that Kuruk's best feat appeared.
In the novel, Kuruk's mentor tells the young Kyoshi about Kuruk first learning to master the Avatar State. He says Kuruk became "a human natural disaster" who unleashed elemental destruction on a grand scale." The first time he entered the Avatar State he went to an uninhabited atoll to practice, and destroyed the entire island by the time he snapped out of it!
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Korra
One would expect the last Avatar in the line of succession to have the most power of all, but unfortunately, Korra's connection to the past Avatars was severed during her battle with Unalaq and Vaatu. She did retain the spirit of Raava that could temporarily enhance her strength though, and in the following two seasons and comics that followed she proved the limitation was not as great as one might expect.
Combined with her ferocity in battle and the fact that she was the first Avatar to master metalbending, Korra proved herself time and again as a powerful bender worthy of defending the world. In her climactic battle with Kuvira's mech she not only produced giant icebergs and hurled enormous boulders at her foe, but even managed to energybend in a move that redirected the mech's building-busting blast of power.
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Aang
Although Aang's pacifistic nature tempers him in comparison to other Avatars, there was quite a lot the last airbender learned to do that made him uniquely powerful. He was the earliest airbending master in Air Nation history, and by the age of 12 developed the air-scooter technique that greatly increased his mobility and speed. Even more impressive, he learned from Toph how to seismically sense his surroundings and from Zuko how to redirect lightning fired at him.
Topping all of that was Aang's development of energybending, bestowed upon him by the Lion Turtle and allowing Aang to remove the bending from any individual he deemed unworthy of its power. That alone could earn Aang the title of the Most Powerful Avatar, but the sequel comic Avatar: The Last Airbender - Imbalance demonstrates his reluctance to use the ability in all but the direst of circumstances. As a pacifist reluctant to use even his best nonviolent move, Aang holds himself back from earning the top spot on this list.
Kyoshi
A legend in her own time and beyond, Kyoshi more than deserves the top spot for Most Powerful Avatar. When Aang followed in her immense footsteps the mythology surrounding Kyoshi towered over him. Not only is she the tallest and longest-lived Avatar in history, but Kyoshi's feet of carving her own island off an Earth Kingdom peninsula and separating it out to see could earn her this top spot alone.
And yet the novel focusing on her, The Rise of Kyoshi, expands on the scope of her power even more. The very first time Kyoshi uses the Avatar State she boils the sea and capsizes several ships with juts of rock from the seafloor, and she goes on to send entire armies fleeing in terror during later showings. Armed with war fans that increase her precision, armor that protects her from arrows and other weapons, and a merciless dedication for justice that pushes her to her limits there is no other Avatar that deserves the title of Most Power more than Kyoshi.