It is always hard to compare national sentiment between countries but it is interesting to see differences in popularity between the UK and the United States. For instance, the Beach Boys were far more popular in the UK than in the United States and maintain a level of critical acclaim there far beyond what they have in their own country.
With respect to the Beatles, things are less clear-cut, but things seem to be pretty even on both sides of the Atlantic in terms of their popularity. The Beatles did have more number one songs in the United States, particularly after 1966, where songs such as Penny Lane, Something, and Let It Be all hit number one, while inexplicably failing to reach number one in the UK. Hey Jude was far more popular in the U.S. than in the UK, staying at number one for 8 weeks, while Hello, Good-bye was more popular in the UK, but both hit number one in both countries. The Ballad of John and Yoko hit number one in the UK for three weeks but was not released in the US, due to its mention of Christ in the lyrics. Eight Days a Week, Yesterday and The Long and Winding Road all hit number one in the U.S., but were not released in the UK while the Beatles were together. The only non-Beatles composed single to hit the top ten wasTwist and Shout. Which was a U.S. number one on the Cashbox single charts, but not Billboard, where it hit number two.
The truly amazing thing about the Beatles on both sides of the Atlantic is that once Capitol Records began handling the Beatles in the United States in 1964, every single Beatles studio LP album of new material went to number one on the album charts in both countries. In the UK, the Beatles had 11 straight such albums, from 1963 until they broke up in 1970, that went to number one. In the United States, where albums were shorter and consequently, they released more of them, the Beatles had all 14 of their Capitol albums containing new studio material go number one, from 1964 to 1970.
This does not include Yellow Submarine, which only had four new songs, and which only charted at number 2 in both the U.S. and U.K. because it was unable to dislodge the Beatles' White Album from the number one spot.