At the end of Revenge of the Sith, Obi-Wan Kenobi defeats Vader and cuts off most of his biological limbs. Since then, he's basically been on life support; he's more "machine than man."
Given Vader's physical trauma, damaged body and his previous defeat, how can Vader be confident of beating Obi-Wan in another duel?
Obi-Wan is comparatively feeble. We don't know exactly how old Obi-Wan is, but he's got at least ten years on Vader. Vader himself notes Obi-Wan's advancing years in A New Hope, and after they initially spar:
Ben makes a sudden lunge at the huge warrior but is checked by a lightning movement of The Sith. A masterful slash stroke by Vader is blocked by the old Jedi. Another of the Jedi's blows is blocked, then countered. Ben moves around the Dark Lord and starts backing into the massive starship hangar. The two powerful warriors stand motionless for a few moments with laser swords locked in mid-air, creating a low buzzing sound.
Vader: Your powers are weak, old man.
Age aside, Vader also has a physical advantage precisely because he's more machine than man: his robotic limbs mean he has more strength in his arms, and Anakin was always about strength over finesse. I'd make the argument that he'd also tire less easily, but I'm not sure canon bears that out.
Plus, Obi-Wan just looks more feeble. Although it's been nineteen years since they last encountered one another1, Obi-Wan looks like a very old man. He doesn't cut the kind of figure you'd expect to defeat a Sith Lord at the peak (or maybe slightly over it) of his power.
Obi-Wan has been a fugitive for decades. After Revenge of the Sith, the Jedi are driven to the brink of extinction by the Empire. As a fugitive from justice, Obi-Wan knew that the only way to survive would be to keep his head down and not get recognized. Believe me when I say that this is not a good way to keep your combat skills sharp.
Vader, meanwhile, has been leading the forces of the Empire. In addition to spending part of the last 30 years hunting down fugitive Jedi, he's also had the resources of the Empire to keep up his skills.
Vader has more practice with the Dark Side. The Dark Side is better at winning duels; I don't think this is a controversial statement. Obviously it didn't help Anakin much in Revenge of the Sith, but by A New Hope he's had almost twenty years to improve.
Overconfidence comes with the territory. Regardless of who is actually stronger, Vader is a Sith Lord. Sith Lords pretty much only do two things in the Star Wars universe:
Try to destroy the Jedi and/or take over the galaxy
Boast about how amazing they are
It's just what they do.
1 Barring some truly delicious retcon
Given that Vader said "I feel something, a presence I've not felt since..." and walks off, there is clearly an unseen connection (likely through the Force) that is explicitly alluded to.
Thus, Vader may have felt directly the inferiority of Obi-Wan's powers and/or feeble biology once they were close enough to duel.
It's also not certain that Vader believed what he said at all. He could have just been bluffing to rile up Obi-Wan, similar to what the Emperor did with Luke.
