Been out of the game for a long time but the launch customer for the GE T700 variant was Italy. Just as the British EH101s were RTM322 powered while the Italian ones were GE T700s. There was little to choose between the two engines so I would think most customers will have chosen based on price.
Having said that, during the development phase the airframer teams internally preferred GE because of its responsiveness as a company. At that time Rolls Royce in particular was thought to be a difficult supplier.