Well, there are a millions of reasons why the Beatles were great, but here's three factors that most people don't think about:
1. Geoff Emerick
He got the call to engineer at the start of revolver. he was still pretty green, but his enthusiasm won everyone over. he broke studio rules to create some of their sounds and could have gotten fired. it was his idea to stuff the bass drum with a sweater and move the mics closer. it was his idea to put the mics in so close on the strings that you can hear the bows scrape for eleanor rigby. he was at the helm for pepper. sir george martin may have been the music man, but geoff should get at least as much credit.
2. Norman Smith
Before Geoff there was Norman, who was at the helm from their very first session until Revolver. He went on to produce, working with among others, Pink Floyd and the Pretty Things. He also recorded his own hit records under the name "Hurricane" Smith. he was the engineer on the Beatles' test session. he helped Sir George decide to give the lads a chance. Legend has it the Beatles didn't really impress the two with their music at first, but rather with their personalities.
3. The Fairchild compressor: this is one of the reasons why "Tomorrow Never Knows", "Rain", and "Paperback Writer" are potboilers, This is why it sounds like the bass drum is activating the cymbals on "She Said, She Said" It makes the music sweat, when done correctly.