These t-bird/Gibson threads are starting to remind me of the vintage v modern threads (or Mac v PC elsewhere)... and as Double Agent said we don't all share the same ideal tone in our heads -- and I don't see any point in putting down others choices to try to validate my own.
I see some statements put out as absolutes when the instruments are very different through different eras; a '60s reverse is different from a '60s non-reverse and both are different from the '70s version (mainly the bridge and the pickups - some people prefer the '70s pups though I strongly favor the '60s ones). And these are very different from the later ones and from the Epiphone versions.
I currently have one '64 reverse and had one other previously (incidentally, relative to earlier comments in the thread, the prior owner being a black player from "back when dinosaurs roamed the earth" - Tyran Porter used that bass on many of the Doobie Brothers big hits -- Tyran-asaurus Rex...) and I had a '66 Epiphone Embassy. I liked the Embassy but the t-bird had the superior tone to my taste, better neck, and stronger resonance - the multi-lam, neck-through construction is a big factor.
You might be right, I tried out 2 60s Gibson Thunderbirds, both had been modified and the necks were thick like a base ball bat, plus those things would have been a Bitch to maintain.
Some of the non-reverses had thicker necks but FWIW my '64 has a very thin and narrow jazz bass type neck that is among the best - to my taste - of the many vintage and modern basses I've had - VERY comparable to a better pre-CBS jazz and the action is as good as any high end modern bass.
No maintenance issues beyond any other bass.
Some say they are tonally "limited" - perhaps controversially, I'd argue no more so than a P-bass (or, more accurately, a jazz bass). With just the neck pickup it sounds very much like a P but stronger. Using the bridge can make harmonics pop, etc but has a thicker - but, despite some comments here, not muddy - character than a standard jazz. Of course they did not have the same level of use on recordings but only a fraction were produced in the '60s relative to Fenders and it is easy to understand why the look is love or hate for many people and that surely reduced their share of the market that much more. As with P-basses (or any other) they really have to be tried out in context to have a full opinion.
They are more fragile than a Fender but that's a choice and doesn't bug me - I play upright too, so an instrument being somewhat fragile doesn't seem too alien to me - much the same as a guitar player opting for a hollowbody rather than the durability of a tele (and it is certainly true that Gibson guitars are more fragile than Fenders in general).
It is true that fret access above the 17th fret is tight - which is a pity as it has the best sounding upper register of any bass I've owned.
Neck dive. No big deal.... relocation of the neck strap button and a wide, suede backed strap and it's a non-issue. I let the neck go and it stays in the same place.
All that said, I've been underwhelmed with the pickups on any of the newer Gibson t-birds I've tried (I've never tried the Epiphone birds)
Myself, I like the look - though I like the tone and feel more - but certainly understand it's not for everyone and that the look rather than the sound could make it seem out of place - it could sound great for country or jazz but, admittedly, would look odd.
Anyhoo... here's mine:
Same bass in use - yes, pretty much sticking to roots but it's what the song called for....
I will say I get a lot more comments on it than any other bass I've used on gigs both from audience members and other musicians (and the sound guys always seem to really like it, too).
BTW saw Pearl Jam over the summer and Ament was playing a lot more than root note pounding on his.