Silver lining to KC-X?

Found this on a website:
“Boeing had initially selected Pratt & Whitney PW4062 engines for its KC-X entrant, but has reportedly considered General Electric’s GEnx engine developed for the 787 and 747-8.”

I’ve never understood why the USAF prefers PW so much when GE clearly beats them so badly (witness the F-16 program). WRT the tanker, if you’re going to buy an engine from 1990, why not buy the best engine from 1990: the CF6-80C2? Better yet, why not buy a modern engine (GEnx) for your old airframe?