My thanks to all of you out there who have provided such erudite responses to my original posting. Whilst I still don't understand quite why there should be such a difference in noise between a GE90 and a Trent, I have certainly learnt a whole lot about the variables and complexities of large turbofan design.
I should point out incidentally that the observations which prompted my original post were based on experiencing 777s coming towards me in a RH turn soon after t/o from LHR 09R. Once the aircraft have passed (almost overhead) there is much less difference in noise between the two, since the exhause roar has taken over from frontal fan noise as the dominant element.
I must say that I am intrigued by the expression "buzz-saw" noise, since it certainly accurately describes that of the Trent (and its RB211 predecessors) but not so much the GE90. It is interesting that a new nacelle intake design is being considered to reduce this effect - I'm intrigued to know how this will work.
If I interpret the various detailed postings aright, this noise difference is unlikely to be due simply to 2 v. 3 spools, or fan speed per se, but rather a number of factors that combine to make a different noise profile. There was a suggestion that the number of fan blades could be relevant, but I have not been able to check on how many blades the Trent has versus the GE90 (actually I did try counting last night as I passed the BA engineering base at LHR last night but it was too dark - sad!!); anyone have any more information in this regard?