We have experimented with both and I can definitively say that rope drop has less crowds and and you get more done than sleeping in / going later. We were sorely disappointed with how little we got done, even with lots of fp's, when we did late arrivals. This was probably because even the fp lines were long and it just took longer to walk everywhere due to the crowds. I would say the majority of people visiting Disney don't even think to arrive 45 minutes before official opening. Most get here around 10 or 11, hence the crowds. Rope drop is a popular concept on these boards, but not one known to the general public.
I would say, if you have lots of park days (7-10) with multiple visits to each park - sleeping in and staying up late is totally do-able. If you only have a few park days (we usually do 4 - one at each park), then rope drop is really the only way you're going to get in all of your favourite attractions. Neither method is right or wrong, it just depends on the length of time you have at Disney and what you are hoping to accomplish.
Until we have enough $$$ to afford 7-10 days of Disney tickets for our party of 10, rope drop 'til close will be our strategy in order to get the most bang for our buck. But I can see this changing as we get older and have more time and money available for trips.