Apart from the recurrence of a few characters, I thought the two trilogies were unrelated.
Except, of course, for that thirty seconds at the end of 'Revenge of the Sith' where they crammed all the continuity stuff. That was one of the worst examples of storytelling I've seen, and I've seen --- yeh verily, I've written --- some unpolished turds in my time.
(While I'm on it, I didn't think the prequel trilogy was that bad. Writing Jar Jar Binks was a far better decision artistically than casting Mark Hamill as, well, anything.)