In addition to what Brendan covered, there are some differences in broad capability between the two powerplants.
The Qantas decision to use GE's on the 767 was somewhat landmark and a cut with the management tendancy of the time -- the 238ERs had PWs, as did the earlier build 742s, while the subsequent 747 fleet (composed of 742, 743 and 74L aircraft) were all RB211-524D4 fitted.
The selection of GE for the 763s as a third major powerplant family was due to its particular suitability to the missions QF intended for the 763s, and the ability for the CF6 to make the commonality argument redunant was pretty significant. This was made even more notable as the 744s entering service just after the first 763 were fitted with the new RB211-524G engine, a very similar choice to the H2 and H4 engines offered for the 767.
The CF6, ultimately, is the most economic of the engines offered for the 767. It's fuel consumption is the lowest in its class, however this benefit is really only found on longer sectors. QF at the time was 8 years from being a domestic operator -- 763s were used almost exclusively on sectors of over 7 hours (SIN to everywhere in Australia, to HKG, NRT and KIX, MNL etc..).
The more robust RB211 is better suited to high sector flying, which is why the ZX fleet was considered a subfleet both in terms of maintenance and operations. They have been dedicated to domestic work since their arrival in 2000 even though the 767 dominated medium haul international work well into the 21st century. The RB211, however also has good (very) mature fuel burn; perfect for the 744 on ultra-long haul sectors that typify Qantas' work with that airframe but perhaps less so for the 767. Most operators used it on sectors about 5-6 hours, which perhaps gives some insight as to why the RB211 was sold in comparatively very small numbers. BA's dominating logic was reducing maintenance costs; I also believe the BA fleet is fitted with -524H2s, making them fully interchangeable with the 744 engines.
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