I am familiar with the RB211s on the 57s - great engine and Rolls is an excellent company to do business with.
The CFM56 is another winner here. Ask any MX guy - this is one reliable piece of kerosene burning machinery.
While I have no direct experience with the 777, I do know that the GE90 is an outstanding powerplant. This engine exceeded customer expectations - not unlike the aircraft it powers.