I have never been impressed by The Beatles. Their early stuff (like The Beach Boys early stuff) is cute, but their magnum opii are underwhelming. I like a few of their finger-picking songs such as Blackbird and Dear Prudence, but especially Julia, which is my favorite Beatles song.
The Beach Boys, for the most part, are excellent background music. I think their surf albums are wonderful and truly capture the zeitgeist. Pet Sounds is flawlessly beautiful. The instrumentation and harmonies are unrivalled. It truly belongs in the Western Canon.
(Edited 1 minute later.)