There seems to have been an unaccountable resentment against them. If you watch the remarks by Mick Jagger when the Beatles were inducted into the Rock and Roll Hall of Fame, there's a lot of sneering in there, about a band from Liverpool, how they all dressed alike (showmanship!), and other assorted petty remarks. He only grudgingly admits that they paved the way for everyone else. I really can't fathom what the source of that resentment is. Richie, though, in true Beatles form, steps up to the microphone and says: "Rock and roll? I though we were a pop band."
Yes, Mick and Keef were always seen as the real down and dirty "proper" rock band in the early days, whereas The Beatles were regarded as the more showbiz and pop of the two. There were many around who, to this day, say that The Beatles (especially Paul) had sold out to commercialism even before they hit the big time. Swapping the leather look (bad guy, serious rocker image) for matching suits and haircuts ( clean cut mummy's boy image)
Meanwhile, The Stones, who started out around the same time, maybe a year later with their first 'hit', took a much more raw approach to their music, drawing on old American blues numbers and taking their lead from Black American Blues artists, like Howling Wolf.
Both bands hit the big time and were almost equally influential in their own way, but it was nearly always the Stones who got the negative press, while the Beatles won the awards from the 'pop' end of the industry.
This battle between the good guys and bad guys of British music was seized upon by the Press, and it generated story after story during the sixties and early seventies.
Therefore, whenever a journalist ever stuck a microphone in front of either Mick or Keef, it was usually an attempt to goad a comment from them as to why they were not as good/nice/succesful/popular as The Beatles.
Sort of "So tell me Mick, do you think that if you wrote better songs, you would start getting awards like the Beatles?"
One, if I remember correctly, went along the line of...."You've just been voted the ugliest rock band in the world. Don't you think it's about time you smartened yourselves up like The Beatles?"
Later on, and in private, they all pretty much mixed in the same circles (London, big houses, Rolls Royces, plenty of exotic tobacco, LSD and willing girls) but in the early days, this light and dark good guy/bad guy pantomime was played out to the full.
Like ticket agents say ...."As long as it puts bums on seats."