Both Anakin Skywalker and Darth Vader used lightsabers during different stages of their lives, and there are some notable differences between their lightsabers.
Anakin Skywalker's lightsaber, also known as the "Skywalker lightsaber" or the "blue lightsaber," was initially constructed by Anakin himself as a Jedi Knight. It featured a blue blade and a hilt with a more streamlined design. This lightsaber was notably used by Anakin throughout the Clone Wars and during his transformation into Darth Vader.
Darth Vader's lightsaber, also known as the "Vader lightsaber" or the "red lightsaber," was an altered version of Anakin's original lightsaber. After his transformation into Darth Vader, Anakin's lightsaber was heavily modified to fit his new persona as a Sith Lord. The hilt was reconstructed with a darker, more menacing design, and the blade color was changed to red.
In terms of functionality and power, there isn't a significant difference between the two lightsabers. Lightsabers are energy swords created using kyber crystals and operate on the same basic principles. The power of a lightsaber primarily depends on the skill and proficiency of the wielder.
However, from a symbolic standpoint, the transition from Anakin's lightsaber to Darth Vader's lightsaber represents Anakin's fall to the dark side of the Force and his transformation into the Sith Lord. Darth Vader's lightsaber is often seen as a more iconic representation of the character and has become one of the most recognizable lightsabers in the Star Wars franchise.
Ultimately, in a hypothetical duel between Anakin Skywalker and Darth Vader, the outcome would depend on various factors such as their skill, experience, and emotional state rather than the specific lightsabers they wield.