On the overall level, having ridden many times on a whole range of types (just like many others here) I find the 777 surprisingly noisy in the cabin for an aircraft of its generation. The A330 and A340 are both notably quieter, even the 747 is quieter inside.
I don't know what Boeing did, the engines for the 777 and the 330 are pretty much the same. Are they mounted closer to the fuselage ?