It wasn't Brian's decision, but he had to go with what the boys wanted. He felt just rotten about having to be the one to tell him he was out and Ringo was in (John said years later that was a mean thing to do to Brian), and Brian tried to include him in a couple of other groups, but Pete told him to bugger off and went with another manager.
About the other so-called "reasons" he got dropped - I believe Alistair and Geoffrey and others who say Brian never made a pass at Pete (unless it was during the short time when Brian knew Pete wasn't going to be a Beatle but hadn't told him yet, and according to Pete during a drive home he just hinted at fooling around and then dropped the subject immediately), and I don't think there was a "cuteness war" between him and Paul.
The fact is, Pete just didn't have a Beatle personality. I can NOT see how Pete could have been a fun guy in those press conferences. His image was to be moody and morose, which the Liverpool girls loved, but the group knew it wouldn't get them anywhere with the greater general public. Pete would have just stood there and glared at the press, or probably would have said corny rather than clever things if convinced that he should lighten up. He's a real nice guy now that he's aged, but still not Beatle material.
About his drumming, I don't know if he was technically better or worse than Ringo -- all I know is that everyone agreed that Ringo had more of a Beatle BEAT to his technique. Ringo fit like a glove. And who else could play the underdog? You gotta have an underdog, and all they had was two "cute ones" -- one happy-go-lucky and one moody. Didn't balance.
It's true the boys knew from the beginning he didn't fit; they just used him in the pre-Eppy days because his mother owned a venue where they could work, and putting her boy in the band was one of her conditions. No need to feel sorry for Pete, he's counting his blessings that he didn't go the way of Lennon or Eppy. He's working steady, our Pete is.
Ringo's doing super, too. I can't wait for his Stan Lee superhero cartoon thingy to come out: what are they waiting for!!! Ringo knows he was America's symbol of The Beatles (Brian even said that in his book - in slightly different words). Even though he realizes he's the "lowest rated" Beatle within their inner circle, he's still a part of history and the phenomenon that changed the world drastically. His name is recognized as being Beatle-ish more than the others. He's always been totally grateful for his lucky break in becoming a Beatle, after what he went through as a child, all the sickness and poverty. He has never forgotten that.
They're both fine. You can look at both of them and be happy.