I myself have not flown on an IL96-300 as of yet. I know people who have, however.
There are a few notable things that have been mentioned. The IL96-300 has a relatively short take-off roll and much better climb than its predecessor, the IL86. Apparently, the plane has a tendancy to roll slightly from side to side while cruising, indicating some sort of stability problem. Also, this is the first Russian-built jetliner equipped with any sort of in-flight entertainment. Aeroflot offers a new movie theatre-style film during long flights with IL96-300s, featuring screens in each cabin. However, there are no separate audio controls or headphones, so the sound is on for the entire aircraft, whether passengers want to watch it or not. I asked specifically about noise levels; apparently, the IL96-300 cabin is as quiet as that of a 767 or DC-10. Apart from that, its cabin layout is very similar to that of the IL86 - 3-3-3 seating in coach, 2-2-2 in business class, and 2-1-2 in first. They typically are arranged to carry 235 passengers in a 3-class layout.
It is a goal of mine to fly on an IL96-300 within the next couple of years. Given my long-windedness in trip reports, you can be sure I'll post about the flight and include every minute detail I possibly can!