I believe the Trent 800 offers the lowest takeoff consumption on the 777-200A/ER, which is in part due to the triple spool design. This combined with its light weight means it is more efficient than the GE90 for flights under ~3000nm, after this the GE takes over (not sure where Pratts come into this). But then again, if you want a 777 to be efficient under 3000nm you should buy an A330-300.
Another advantage of the triple spool design that an engine family is extremely scalable.
Note that the RB211 has ranged from the -535 at ~37klb to the -T800 with ~94klb. RR also hoped to supply an engine for the 777LR program which demonstrated 114klb in test but were denied a place due to engine exclusivity.
This scalability has proven crucial though as it has allowed RR to not only supply engines for the 787, but exclusively supply them for A350. So even though the 787 order books so far say the GeNX is a better package than the Trent, RR stands to dominate the upcoming generation of widebodies.