Why did Obi-Wan disappear instead of being cut in two pieces?
Obi-Wan knew the secret to becoming a force ghost.
Anakin (Vader) didn't actually die.
2.5. If they had made it so Anakin (Vader) used the force to recreate his missing appendages, they could have been liable for lawsuit from the creators of The Venture Bros.
The quote below is taken from the Star Wars wiki, apparently Qui Gon Gin rediscovered the force ghost ability and Obi Wan developed the technique of one's body disappearing. He even taught Yoda how to do it. Unfortunately the wiki does not cite where those paragraphs come from.
Death for those Jedi were different: their spirits could retain their individuality and could return as voices, dreams, or apparitions at will, so that they could help those in need of their guidance. On death, their bodies vanished; this was not the case with Qui-Gon, however, probably being a technique evolved by Obi-Wan and Yoda, under Qui-Gon's guidance.
Darth Vader learned of this ability through Darth Sidious, and upon his death, the spirits of Kenobi and Yoda completed his training by granting him the last step in becoming a spirit. Anakin's spirit appeared as that of his younger self, prior to his fall to the dark side.
It is also likely that the age of the film impacts this. Perhaps Lucas had some scrapped idea for Obi Wan. Not knowing just how big Star Wars was going to get.