The jousting that went on between The Beatles and The Beach Boys in the mid 60's went like this, pretty much due to the shear chronological time frame of each album's release dates.
The Beatles - Rubber Soul
Recorded: June 17th; October 12th – November 11th, 1965
Released: December 3rd, 1965.
The Beach Boys - Pet Sounds
Recorded: July 12, 1965; November 1, 1965 – April 13, 1966
Released: May 16, 1966
Brian Wilson and the Beach Boys are so impressed by Rubber Soul they go ahead and create Pet Sounds (I imagine primarily in the period of time between November '65 and April of '66 since presumably hearing all of Rubber Soul in December).
The Beatles - Revolver
Recorded: April 6th - June 21st, 1966
Released: August 5th, 1966
The Beatles, after hearing The Beach Boys Pet Sounds in May of 1966, wrote and recorded much of this album which is seen as a reaction to it.
The Beach Boys - Good Vibrations (Single)
Recorded: February–September 1966
Released: October 10, 1966
After hearing The Beatles Revolver, The Beach Boys, or rather Brian Wilson specifically reacted so strongly with trying to top that album, he wrote and had the band go through an incredibly meticulous and expensive process to make this single song.
"The production of the song is reported to have spanned seventeen recording sessions at four different recording studios, and used over 90 hours of magnetic recording tape, with an eventual budget of $50,000."
Originally, Brian Wilson never intended this to be included on a full-length LP, but in the process of making the music for Smile, and also the reaction to The Beatles Revolver, it was then intended to be included on Smile.
The Beatles - Sgt Pepper's Lonely Hearts Club Band
Recorded December 6th, 1966 – April 21st 1967
Released: June 1st, 1967
The Beatles released this as a reaction to The Beach Boys Good Vibrations, but also a follow-up to Revolver.
The Beach Boys - Smile/The Smile Sessions
Recorded: May 11, 1966 – May 19, 1967
Except "Good Vibrations": recorded February 17 – September 1, 1966
Released: November 1, 2011
So if you're one of these people who thinks Pet Sounds or even Smile was part of the jousting from Sgt Pepper's Lonely Hearts Club Band, take a look at the actual RELEASE DATES and you may realize you're off by 1 album.
However, based on the dates Smile/The Smile Sessions were actually RECORDED, Brian Wilson and The Beach Boys hadn't even heard Sgt Pepper's, because they finished recording for Smile a few weeks earlier in May.
The ole story goes is when Brian Wilson heard Revolver he freaked out so much he labored for all that time over what never got released until this year in The Smile Sessions. Then after completing work on that, he heard Sgt Pepper's and decided to give up. But it was REVOLVER not SGT PEPPER'S that inspired Smile. Sgt Pepper's was basically just salt in his already deep wound.