I guess they evaluate each engine by examining the specs and how each affect the performance of the aircraft: cost, weight, fuel burn, thrust generated,... It all depends on the operations of the airline, how much cargo they carry, how the aicraft is configured, routes flown. Example: if we choose the PW over the GE then the 747 will weight that much and that much thrust will be generated, after a 12hr flight at FL350 that much fuel will be burned,...see all these things are taken into account.
It also depends on the relationship the airline has with the engine manufacturer. It is no surprise that United chose the PW 4056 for it's 747-400 fleet because of the long-time United-Boeing-Pratt&Whitney relationship. Northwest also by principle chooses PW engines on all of its Boeing products. British Airways, Cathay, Qantas and South African Airways chose the Rolls Royce power plant, it's normal since they are carriers from a country under British influence. (now why BA chose the GE engines for the 777, that I don't know).