I'd say that usually my enjoyment diminishes drastically, but there were a few games I still enjoyed the second time round, usually because there's a gap in between playthroughs.
There were also a few games I enjoyed more the second time round, because parts of what I remembered helped me to pay attention to other details the second time round.
Generally though, the less I remember from my first playthrough, the greater my enjoyment is during the replay, and vice versa for lack of enjoyment.
That said, with limited time and a growing backlog, I think it's probably a better use of time to stick with new titles.