Depends on your venue and the instrument you are talking about. I assume you mean RM's 370-12, as none of the other Byrds played RICs.
Speaking from personal experience, and from watching the Byrds live in 1966, I would go with the Fender BF Dual Showman. RM used it on stage for his 370-12. It takes the top of your head off at full volume.
Of course, that was in the day when live venues had PA systems for vocals but not instruments. Depending on the venue, you could probably do just as well (if not better) today with an amp having slightly less wattage. For a RIC 12-er, if you limit yourself to 1965 Fender BFs, I would think the Twin Reverb or Super Reverb would be a good choice. The Deluxe and Princeton Reverbs, with lower wattage and one speaker each, don't quite do justice to a RIC 12-er.
I'd shoot for the Super Reverb or Deluxe Reverb, mostly because they're not too small (Princeton, Champ) and not too loud (Twin, Twin Reverb). With the right compressor (Janglebox, Boss, Danelectro Surf and Turf), a hollowbody 12-string in the bridge position and flatwound strings, along with your choice of blackface reissue, you should be flying high (bad pun intended).
I'd suggest the Twin; Brian Medway uses one exclusively when playing his Rick 12s IIRC, and I think they sound beautiful with a Rick 12 going through them. I think the circuitry between the Dual Showman and the Twin are pretty much identical; the only difference I can think of is that one is a separate head and cabinet piggyback combo with either a 2x12 or 2x15 cabinet, while the Twin Reverb is a 2x12 "suitcase" style combo amp. Other than that, the control layout, circuitry, and wattage are the same.
It really all depends on what you're doing with the amp. The Twin is almost overkill wattage-wise-my AC30 has more than enough power for live playing with Smiling face down, but I like the fact that my amps do not have to work all that hard to produce the tone I want; consistently pushing one's amp is sort of like driving one's car at high speed all the time-more wear and tear. I also prefer the bigger, more balanced sound that, to my ear, an amp with 2x12 speakers produces compared to 1x12 cabinet. There's also the Pro reverb option, IIRC, which is like the Twin but with half the wattage. Amp tone is subjective, and preference for a particular setup is a personal choice, so compare your fellow forumites experience with your own observations.
Of further note, some forum members have an issue with weight in regard to the bigger amps such as a Twin, so when you go look at amps, pick one up and see if it's of a weight that you're comfortable with carrying. I usually use a four-wheeled furniture dolly, or else an Anvil case with wheels (better!) to roll my gear around on, but you'll have to pick it up and put it down at some point, whether its to carry it up/down a flight of stairs, take in/out of the car, or place on stage, so make sure you're comfortable with the wait. I suggest ALWAYS bending the knees, not the back, and carrying the amp "bear hug" style; holding it in front of oneself with two hands on either side end of the amp, rather than holding it in one hand suitcase style at one's side where it can tire your arm out and knock your knees and ankles! Carrying the amp "bear hug" style makes for a much more comfortable, balanced, less stress on the body mode of carrying the amp.
I use a Twin with my 360/12. It sounds great. It's plenty loud (if necessary), and yet not too cumbersome to transport, etc. You can get the big sound out of it, despite its relatively small size.
As Paul mentioned I have used a Twin Reverb exclusively for my 360/12 WB for both recording and live situations. The Fender Twin Reverb does the trick for me. I rarely uses any pedals of any sort when I play and I also do not add post recording effects either, so it is critical for me to have an amp that produces a sound that is both pleasing to the ear and that is robust.
My advice is to try a few amps in your local Fender store until you find something that works for you................we can give you opinions all day long but there is nothing performing like A/B tests with your own guitar.
Roger used a Roland JC 120 for years............you may want to consider one of those.
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