I want to get one of them to play the best band in the world, The Beatles. The question is, which? And don't say, "Which Beatles era do you like best?" because I LOVE every Beatles era.
You should go to a store and play them both. I prefer Ric guitars to Epi guitars. I still love Epi, but those Rics are to die for.
Telecaster - SG - Jaguar
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P-Bass - Mustang Bass
Apogee Duet 2 - Ableton Suite
They are tonally VERY different guitars. The Casino has a nice chime to it, but has quite a lot of depth. The Ricky however, is very trebly. It's a very unique tone that you can hear distinctly in the Beatles and many mod classics and specially in The Smiths.

The Ricky is such a beautiful guitar though, I'd go for that. I love Casino's...but compared to a Ricky? No chance.
Ibanez PGM301
Ibanez GRG170DX
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Boss GE-7

Orange Rocker 30 Combo