I'm familiar with the Fab Faux; there are five of them, not four, all studio pros for whom the FF is a side project, not their main gig.

There's a really good Beatles tribute group in the New Orleans area called Penny Lane. They've apparently been together for 20 years or so, but I was completely unaware of them until fairly recently. They don't look like the original four Beatles, but each member does manage to sound amazingly like his counterpart. And, they make it a point to own and play the exact vintage gear ~ violin-style bass for "Paul" (played right-handed), Rickenbacker guitar for "John," Gretsch Country Gentleman and a couple of other guitars for "George," etc. They also have a couple of sets of costumes, depicting different Beatle eras, and change clothes during their breaks.

The drummer doubles on some kind of sythesizer which allows them to recreate the later studio recordings fairly well.

The band was invited to play in Liverpool a year or two ago for the big anniversary celebration; they got to play in The Cavern (!)