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Northwest uses the CFM-56-5 on their fleet, same engine family as the 737 series, CFM International is a consortium of GE and French manufacturer SNECMA.
United uses the International Aero Engines V2500, also seen on the rare MD90s. IAE is a consortium of Pratt, Rolls Royce, Japan Aero Engine, and MTU.
They two are not vastly different, they are both avalable in the various thrust ratings offered by Airbus, as litle as 22000 lbs on the A319 and up to 33000 on the A321. And there has been no rhyme or reason as to engine selection by operators. UAL has hundreds of CFMs on ther Guppies, but selected the V2500 despite the reduction in commonality. Similarly British Airways chose IAE over CFM despite owning a fair number of CFMs already. Meanwhile Northwest, who doesnt do anything frivolous, was in a position to select the most strictly economical engine since they had neither powerplant in their exisiting fleet. They chose CFM, but that makes UA and BA's decision look strange, for why would they add another engine to the stable if there wasn't a conclusive advantage?
I guess the conclusion to be drawn is that in many purchasing decisions the product is basically equal, then it just comes down to which seller is more motivated.
Interestingly, when it came time to develop the A340, Airbus signed an exclusive agreement with CFM. Who knows.