Initially, the CF6-80C2 was clearly the better engine choice for the 767. However Pratt was finally forced to redesign the HP compressor in the PW4000/94" to address compressor surge issues. It's been a while, but I'm thinking we certified the Ring Case Compressor (RCC) around 2003 or 04.
The RCC solved the surge issues, and had the additional benefit of improving efficiency and hence fuel consumption. The RCC was AD'ed by the FAA to solve the surge problem (which had a bad habit of occurring during Takeoff), so all PW4000/94" engines still in operation should have the updated compressor. With the RCC the PW4000 was at least the equal of the CF6-80C2 - but as for market share it was basically too little, too late.
The RB211-524G/H was never a good match to the 767 - for reasons that were never completely clear to me it was not nearly as good on the 767 as it was on the 747-400 compared to the GE and PW offerings.