400R, your figures are a little exaggerated. If you are talking about comparing the RB211-524 in comparison to the CF6, the weight difference is significantly less than a tonne (the -T mod reduced the weight as well as lowering fuel consumption) but more importantly, the engine "hot section" lasts more than 2 times longer than the GE - the difference is so large that GE has been doing a lot of research into extending the life of their "hot section" and a mod has recently been released (although this will still not be as effective as the -T mod). The slower decay of the "hot section" on the RR results in better fuel consumption figures which more than offsets the weight difference.
If you want to look at higher thrust engines as on the B777-200ER/300 which I believe are in the 95-98,000lb thrust class, the GE90 engine is more than 2 tonnes heavier than the RR Trent, so it appears that the 3 spool design becomes more effective at higher thrusts.
The residual thrust is less (so on flare I always retard the levers at 30ft for the Rolls) c.f. 50 ft for the GE's, and as it is company policy to shut down 2 engines on arrival after the mandatory cool down period, the Rolls always requires more than idle thrust to keep the aircraft moving.
You obviously have a different flare technique to me and I find the Roller a much easier aircraft to get consistent landings. The higher residual thrust of the GE's tend to cause longer landings unless you use the half flare & freeze technique. Taxiing the RR aircraft at 15-18 knots does not require more than idle thrust but if you dawdle around at 8 knots, then you have to apply additional thrust. The high idle thrust of the GE does cause significantly more use of the brakes which is not ideal.
The GE is a great engine wrt its faster starting and better acceleration but talking to a number of LAME's the RR is machined to a higher standard.
Getting back to the thread, it's hard to do any comparison on the B787 engines at this stage as both engines are significantly different due to there being no requirement for huge quantities of bleed air. Qantas selected the GENx engine over the RR Trent 1000 but I recall Peter Gregg saying at the time that there was very little difference between the engines.