Sam711,
The RR 767 engines are rated for 60600lb thrust - slightly higher than the GEs, though in practice, the GE aircraft accelerate and climb (even) better.
The RR engines are heavier, and the aircraft also have higher basic weights. In answer to your question, RR or GE variants aren't necessarily put on certain routes for performance reasons. In any case, most of the MEL - SYD - CG- BNE 767 flying is done by rollers; most PER flights at the moment are being done by 200s. All the international flying is done by GEs, with the exception of some NZ flights with RRs, and Noumea services done with the -200.
Either way, the aircraft are overpowered to *******, so performance isn't an issue; The RR aircraft have higher seating capacities (about 254 pax in 2 class config compared to around 229 for a GE -300). Just to confuse, OGV also has the high capacity config. The GE config cabin is more suited to international routes, and these aircraft also have a 180min ETOPS approval compared to 120min for the roller and pratt.
As mentioned, 4 of our GE machines have gone north, so there will be fewer and fewer of them flying domestically.
WG.