Is the improvement at the expense of greater interior noise?
It will be a decade or more before folks forget how quite the A380 is and make the comparison.
No. Because the engines are positioned further from the fuselage when compared to the classic 777 which will help with noise. It also has a newer engine with lower thrust, which again will help with noise. Thirdly the plane is also more aerodynamic when compared to the 777, which again will reduce noise.
The 777x is an all around improvement from the 777 in almost every aspect. How much improvement? we have to wait and see until the plane enters service for real world comparison.
No, because better noise insulation was developed too.
Partially, the engines will have more sound absorbing material. Quite a bit has been learned from the business jet aspect. The GV (early gulfstream V) had the area buy the engines (couches) so loud, they really weren't usable. Same with the early global express. Then bombardier upped the insulation on the Globals (in particular, back by the engines) and Gulfstream had to follow with the G650. The high end business jet market now demands cabin noise under 60db. http://www.luminary.aero/blog/quiet-aircraft-cabin/
Commercial aircraft are 65-80db. They won't go higher as US OSHA laws apply and if F/As or other airline workers are exposed to over 85db, that is a HUGE lawsuit. The A380 is on the low end.
I expect the 777X to be quieter than the 77W, but not by much. I do not expect it to be as quiet as the A380. Cest la vie.
You know nothing John Snow.