I think i know the answer to this but im not sure
The RR engine has a long fan duct which has lower drag than the PW model, but the extra long fan duct also adds weight.
For carriers that do mostly long haul flights, the RR might be a better choice because of a lower fuel burn. On the other hand, the PW might be a better choice for a high density short distance carrier because the aircraft has more usable payload.
Of course there are a bunch of other variables that go into engine selection for an airline like specific fuel consumption.
The only figures i have give the RR RB.211 a SFC of 0.57 and the PW 4152 a SFC of 0.58. For those of you new to engines, SFC is the pounds of fuel burned divided by the pounds of thrust developed. The lower the SFC the better.
The same source also claims the RR makes 60K trust versus 52K for the PW. However this is hardly comparing apples to apples so it doesnt mean long fan ducts are the way to go.