We have always done late dining but I'm pretty sure it is the same as early.
We all enter the dining room at approximately the same time, you sit at the same table with the same servers and have the same menu. Probably have the same "entertainment".
On our cruise in February there did seem to be more empty tables than we were used to seeing.
A Bad Day At Sea [with power] Always Beats A Good Day At Work
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014