Trivia: Originally Obi-Wan Kenobi survived the duel with Darth Vader and fled aboard the Millennium Falcon. But the character had very little to do with the rest of the film, and George Lucas decided that he should be killed off. Alec Guinness threatened to quit the production over the change, but Lucas convinced him that the change was better for the overall story.
Trivia: Sir Alec Guinness was apparently not a fan of the Star Wars dialogue. A letter was found in 2016 that he wrote to his friend saying "New rubbish dialogue reaches me every other day on wadges of pink paper, and none of it makes my character clear or even bearable."
Trivia: Princess Leia and Obi-Wan Kenobi never meet once in the entire film.
Trivia: When Luke is the climbing the ladder to his X-Wing fighter before the Battle of Yavin, an InCom Engineer asks him if he needs another Artoo unit. This engineer is Shane Rimmer, best known for the voice of Scott Tracy in the Gerry Anderson series "Thunderbirds".
Trivia: George Lucas was so physically exhausted after shooting this film that he did not direct another film – not even the next two Star Wars episodes – after that. It wasn't until 1999 that he returned to the director's chair for Episode I – The Phantom Menace.
Trivia: Scenes with the Jawa sandcrawler were shot near the border of Tunisia and Libya. Worried Libyan officials looked over the vehicle to make sure it was not part of a Tunisian military operation.
Trivia: Although Peter Cushing is listed as Grand Moff Tarkin in the end credits, he is never referred to as either Moff or Grand Moff. Throughout the film, he is simply called Governor Tarkin or Tarkin.
Trivia: Before being cast as Darth Vader, David Prowse was offered the role of Chewbacca. Prowse turned down Chewbacca, as he did not like the idea of having to wear a furry monkey costume for his part, so he chose Darth Vader, as he believed that everyone remembers the villain.
Trivia: Luke Skywalker only uses his lightsaber for a little bit of training with the floating orb in this first film; he never actually fights with it until The Empire Strikes Back.
Answer: It is heavily implied that one who becomes a Force-Ghost achieves an untold level of power upon entering the state. Given that they have become a pure entity of the Force, it seems to back up the statement. Obi-Wan also becomes free to assist Luke in any case.
Darius Angel
In addition to this answer, I think Obi-wan also became powerful because he "let go." He did not feel a need to defeat Vader on this occasion - he was willing to surrender the fight and "move on" to a new state. Something that Vader might not currently understand.