I was never a big Bruce fan. I would vote for the Eagles and the Beach Boys. Brian Wilson was incredibly creative, and never got enough credit for it.
His own jealousy of the Beatles drove him crazy though. Damn shame
I don't think the Beatles caused him to undergo mental and emotional problems. The Beatles were astounded when the Beach Boys came out with Pet Sounds. He and McCartney were good friends and admired each others' work openly and honestly. McCartney has long said that Wilson's God Only Knows is the most beautiful song he's ever heard, and Wilson was moved to tears when McCartney first played a demo of She's Leaving Home for him before Sgt. Pepper was released.
Also, Wilson kind of inspired McCartney to write Back in the USSR as they joked about a Soviet version of Chuck Berry's Living in the USA. The Middle eight of Back in the USSR is McCartney's tip of the hat to the Beach Boys' California Girls.
There was certainly competition between the bands, and as good and innovative as the Beach Boys were, they certainly realized they were not on the same level as the Beatles.