WARNING: The following contains spoilers for the Attack on Titan manga by Hajime Isayama, available in English from Kodansha.
In the world of Attack on Titan, the power of the Nine Titans reigns supreme. While most Titans are mindless man-eaters, the Nine are sentient, human-controlled Titans that possess unique characteristics and abilities that make them the most powerful beings in the world. Even though the Founding Titan is the original Titan and possesses omnipotent power over all Titans, the Attack Titan is superior thanks to its ability to make a more direct impact on the world, free of the various restrictions that inhibit the Founding Titan.
The Nine Titans each possess unique traits that make them tremendously powerful. Despite how different they each are from one another, the one thing that most of them have in common is that they have been defeated by the Attack Titan. The Attack Titan has fought and defeated the Founding, War Hammer, Armored, Female, and Jaw Titans. The only Titan that the Attack Titan has fought and lost to was the Colossal Titan, due only to the immense difference in size. Only the Beast and Cart Titans have never been in direct confrontation with the Attack Titan.
The Attack Titan's physical strength is even more impressive given that it has no gimmicks or special abilities. It's average-sized, does not have full-body armor or sharp teeth, nor can it summon or control other Titans. The Attack Titan just has hands that are rated "E for Everyone." While it did gain a hardening ability, a lot of the credit goes to Eren's dedication to combat training and his incomparable willpower. However, even when the Attack Titan was in the hands of Eren's father, Grisha, who was by no means a fighter, the Attack Titan could still overpower and kill the Founding Titan.
Other than the Founding Titan, the Attack Titan appears to be the only Titan that influences its user. Eren Kruger, the Inheritor who preceded Grisha, described the Attack Titan as having pushed ever forward, always fighting for freedom. His bold claim is backed up by the fact that the Attack Titan was one of only two Titans to never fall into the hands of Marley during the Great Titan War. Marley spent countless decades utilizing the power of seven of the Nine Titans, and while the Founding Titan stayed in the hands of the royal family on Paradis Island, the Attack Titan's whereabouts remained unknown for centuries.
The Attack Titan is more than just an elite fighter, it also possesses a secondary ability that puts it in a class all its own even amongst the Nine. The Attack Titan has the ability to transcend time. While all Titan Shifters can see the memories of previous Inheritors, the Attack Titan has an ability that allows the current Inheritor to send their own memories to previous Inheritors, effectively allowing that person to see the future. This remarkable, god-like ability is solely responsible for every single event that transpires during Attack on Titan.
At first, sending memories to the past sounds insignificant and fairly limited in its practical use. However, Eren used this ability to goad his father into killing the royal family and stealing the Founding Titan. When Grisha found himself unable to go through with it, Eren showed him his own memories of the future ahead of Grisha. This allowed Grisha to see the future in which his wife would die in an attack by Marley's Titans, which gave him the final push he needed to carry out his attack on the Reiss family, which served as the catalyst for Attack on Titan's entire story.
Furthermore, the current Inheritor of the Attack Titan can choose which memories to send to the past and can even send only partial memories to manipulate the previous Inheritor. Eren used this ability to effectively control the flow of history in such a way as to best suit his ambitions. Controlling Time is no small feat, and it's something Eren has been doing behind the scenes for the entirety of Attack on Titan. When he kissed Historia's hand, he saw his father's memory of receiving memories from Eren in the future, giving present-day Eren an omniscient awareness of everything that would happen going forward.
Eren's manipulation of time with the Attack Titan's ability is ultimately what lead him to obtain the Founding Titan, which results in the eradication of Titans from the world. Eren's mastery of the Attack Titan's incredible power makes him responsible for the events of the entire series. Even the Founding Titan has not had as profound an impact on the world, making it clear that the Attack Titan is truly the most powerful Titan.
