Vader is always in his fighter when you use him in space. After all, there wouldn't be much use in keeping him cooped up in a Star Destroyer where none of his abilities could come into play.
No one can ride in the Death Star. It is a background unit that can destroy planets and spawns Victory-class Star Destroyers. It cannot fire on enemy ships, and they can't fire on it.
"We think in language; therefore, the quality of our thoughts can only be as good as the quality of our language."
-- George Carlin