Pet Sounds was released before Sgt Peppers. Some might suggest the Beatles (and the Stones with His/Her Satanic Majesties Request) was their effort to keep up with the Beach Boys.
Inspired by the Beatles' Rubber Soul album, Wilson set out to construct the greatest pop record ever made.
Bruce Johnston, the sixth Beach Boy, was in London and played it for John Lennon and Paul McCartney. The two Beatles were both inspired to expand their songwriting and recording skills, culminating with Sgt. Pepper's.
And Brian was quite pleased with Pet Sounds, but supposedly after listening to Pepper's felt as though he had been surpassed. It went down hill from there.
Just my recollection, I do enjoy both of their works.
Their worst effort by a longshot. Thankfully they followed this embarrassment with perhaps their best effort and undoubtedly the first of their releases that was quintessentially Stones -- Beggars Banquet. .....the first of a series of four of the best albums in the history of the genre, imo.
Pet Sounds was the response to the Beatles (Revolver or Rubber Soul, can't remember which).
SMiLE was to be the followup (which originally would have preceded Sgt. Peppers' but it kept falling back in production).