As a Padawan, Anakin Skywalker went through the traditional process of traveling to the Jedi world of Ilum to seek out a kyber crystal and construct his very own lightsaber. However, Anakin actually had two lightsabers during his Jedi career, with his second becoming far more important with a very complex legacy.
Anakin Skywalker carried this blue-bladed Jedi weapon throughout the Clone Wars. After dueling his former apprentice on Mustafar, Obi-Wan Kenobi took Anakin's lightsaber and kept it on Tatooine for nearly two decades. He gave it to Luke Skywalker, who lost it when Darth Vader struck off his son's hand in Cloud City.
During the First Battle of Geonosis, Anakin made use of a green-bladed lightsaber lent to him by another Jedi named Nicanas Tassu, but it was destroyed during a duel with Count Dooku. At some point between his ordeal on Geonosis and the mission to Benglor, Anakin Skywalker built himself a new lightsaber.
He tracked Jedi Master Kirak Infil'a to the river moon of Al'doleem and confronted him. Vader eventually killed the Jedi Master and retrieved his curved-hilt lightsaber. He headed to Mustafar, where he bled the lightsaber's crystal, turning it from green to red.
By the time Rey touches the weapon, Anakin has long been redeemed, and the essence inside the Skywalker lightsaber is constantly calling her to learn the ways of the Jedi and fight against the dark side in his place.
Meanwhile, Anakin is the only one with substantial training; he was recruited as a child and trained as a padawan in the Jedi Order in a more traditional way, as shown in The Phantom Menace and Attack of the Clones. Admittedly, Rey skills couldn't possibly be as developed as Anakin's or Luke's.
Although Rey is also strong with force, she doesn't compare to Anakin's pure strength with the force and his connection, being created by the Force itself. Even in the movies, comics, and shows we see Anakin accomplish greater feats of strength that Rey was years away from learning.
Anakin Skywalker wielded 4 different lightsabers across the Star Wars timeline (including his years as Darth Vader). One of the galaxy's most powerful Force-wielders during the prequel and original trilogies, Anakin Skywalker was incredibly gifted with a lightsaber as well.
Anakin Got His Scar From Dooku's Apprentice, Asajj Ventress
Ventress, one of Dooku's deadliest assassins, seeks to kill Vos for his actions; however, she is unable to get to him. Instead, she settles for a Jedi she can find: Anakin Skywalker.
Another big question the sequels declined to answer was how Maz Kanata came into possession of Luke Skywalker's blue lightsaber. Rey found the saber in a basement storeroom of Maz's castle.
This explains why Rey could hear the lightsaber "calling" to her in Star Wars: The Force Awakens; she was destined to join herself to the same Skywalker legacy, and thus she was sensing echoes of Anakin and Luke beckoning her to them.
As Kylo Ren, Ben briefly used Anakin's lightsaber to kill a Praetorian Guard, but after returning to the good side, Ben was given the weapon once again by Rey.
Qui-Gon's apprentice, Obi-Wan Kenobi, then used the same lightsaber to defeat Maul after losing his own. After the battle, the weapon was later returned to the Jedi Temple. With the advent of the Great Jedi Purge, the blade again fell into the possession of Kenobi, who went into hiding on the planet Tatooine.
See, Anakin built the lightsaber. He owned it. He used it to defeat Dooku, disarm Mace Windu, and kill younglings. The lightsaber was taken by Obi-Wan and given to Luke, and then later found by Rey.
When he originally joined the Sith, Darth Vader simply continued wielding his second lightsaber that he created as Anakin Skywalker. However, this lightsaber was taken from him by Obi-Wan Kenobi after his defeat at the Jedi's hands on Mustafar. Deprived of his weapon, Vader was forced to create a new one.
When tallying up the lightsaber losses, Obi-Wan Kenobi lost his blade a total of 12 times between the events in the prequel films and The Clone Wars. In contrast, Anakin lost his only eight times.
A notable Jar'Kai master was the Priapulin Jedi Master Skwelli, who carried six lightsabers. He was renowned for his skill in his era, and recordings of his fighting form were considered a wonder to behold.
In a galaxy filled with lightsabers of various colours, the Darksaber stands out as the rarest lightsaber colour, shrouded in mystery and steeped in history. Created by the first Mandalorian Jedi, it has passed through the hands of warriors, terrorists, and heroes, leaving an indelible mark on the Star Wars universe.
Kylo lost to Rey in TFA because he was heavily wounded and was holding back against her due to Snoke's request that he bring her back to him alive. He is also stated by Palpatine in the Secrets of the Sith book to be “equally as powerful as a real Sith despite not being one”.
Despite being the Chosen One, Anakin Skywalker was not the most powerful Jedi in Star Wars, as that honor goes to Ahsoka Tano. The Star Wars prequel trilogy focused on Anakin's desire to become the most powerful Jedi, and while he became very strong in the Force, his lust for power drove him to the dark side.
He has decades of experience and even though Rey's brute power has seen her through every fight, Vader has the power and the skill, something Rey lacks in comparison. Rey just couldn't match up to Vader.
