When you consider the whole ~ decade they were together as a group, I wouldn't say "pop OR rock" I'd say "MORE than just pop or rock" Very few bands reinvented themselves so much, but Queen is another example. You simply can't put them into a single genre when you look across their repertoire.
Consider just a small sample of their songs - Yellow Submarine, Oh Darling, A Day in the Life, Her Majesty, Sgt Peppers, Mr Postman/Please Please Me, Lady Madonna, Magical Mystery Tour. Then compare with Queen (eg. Bohemian Rhapsody, Crazy little thing, Killer Queen, Somebody to love, Gotta Break Free, We R Champions etc.) or Billy Joel (uptown girl, piano man, just the way you are etc etc) to name a few - they are just too versatile to cram into a single genre. Elton John is another one who would fit into several genres.