Well I have an AX80, JX-3P and JX-8P. Owned them for quite a while and now it's coming time to sell I've gone round in circles a bit.
JX-3P is special to me still as it has this vibe that I really like, it has character, I don't think I can sell this BUT it's easily the least powerful of all the listed synths. ALL 3 (4) synths are different!
First the 8P/JX10 is the classiest sounding, the smoothest (in a subtle warm almost digital pad way with some analog tone present) however, aside from it's pads, and if you won't use those strings/pads a lot, it's my least favourite of the 3 (i'm counting 8P and 10 together cos the layering is just an extra feature, I can easily layer 2 JX-8P tracks if I wanted, this is about the sound).
I would take 8P over JX10 (and not just because it's more enjoyable ergonomics wise) but because it really does sound a bit more pleasent on like for like pads (and a guy with golden ears who works in the industry told me he also prefered the sound of the 8P while the guy he programmed synths for owned a JX10, the JX10 owner's initials are NR who used the JX10 on his band's 1986 album and and a bit on their 1988 album - don't wanna get to specific here but as I said not just my ears).
JX10 looks great as is nice to own if you want the daddy of the JX range, if you can get it for not much more than 8P then get it - while *I* prefer the 8P because it's more a joy to own, I don't think the audio difference or the pains of JX10 owning would be enough to put you off one way or the other if you didn't have a previous preference. Layers may be nice, but tone/patch management is no joke, it's not fun. You could think of it as a 12 voice JX-8P with cleaner (less 'analog' sounding) output and shit midi if you prefer.
AX80, for me, is hands down the most interesting synth of the bunch. It's the only one with PWM (and you can sorta 'fake' PWM on the JX's but... hmmm). AX80 doesn't sound 'sweet' like the JX's though. Completely different sound! Ignore what you read about it being similar to JX3P that is only on paper.
So, for me JX-3P and AX80 are the best UNLESS you require glossy, classy pads with some nice atmospherics and the best keybed (and overall features like portament/unison etc) of the lot.
Me, I'm more about individual sounds and individuality and the AX80 can sort of sound a bit moogish or a bit p600 or a bit this and a bit that however it really does, when you get to know it, offer more interesting sonic posibilities for today's recording. It sits well in a mix too. It's output is as clean as a whistle (prob cos it has no built in chorus etc) and it's got punchy bass that none of the other 3 can dream of (JX-3P would be the next most punchy).
8P/10 can sound a bit false after a while, not sure what it is about them. Really you have to want THAT sound, but personally I could do much of what the later JX's do with digital and then some, in the mix it would sound 9/10s the same. 3P and AX80 couldn't be done quite so easily with digital, they both have character and attitude.
Really though, they sound so different from each other than the only way to know what you would like is to try them all! I can easily imagine many people not wanting harder/quirky bass or harsh filterage (CEM 3372) of the AX80, or the retro metallic bouncy sheen and ambient filterage (IR3109!) of the JX3P and preferring the mellow/classy/epic pads of the 8/10 (unfortunately, the filters in the 8/10 are one of it's worse aspects, lifeless and ordinary with very weak resonance)
That's probably why I ended up with all 3 in the first place.
AX80 would be the last one I'd sell as it's the most interesting/exciting to me, I love programming it and putting it through outboard as it really carries it's signal well inspite of it's somewhat weak oscillators, it's filter is way more aggressive than JXs and can self oscillate
And I'd probably even sell a polysix before the AX80 (and the polysix has a great tone, if a bit simple) again because AX80 is more unique and less overused compared to the JXs.
I'd look for polysix, AX80 or JX-3P before considering an 8/10 unless, as I said, I wanted smooth DCO pads that are verging on digital in sound, it's less interesting overall though it can do a large variety of sounds inc bass, leads, drones etc but they all sound a bit less than what other synths can do... ahhh really there's no right answer it's all about taste.
EDIT > 1.5 years later - I sold the AX80 so forget what I said above. The JX-3P still gets my vote over time, I couldn't get rid of it and I sold the AX for a nice profit when I needed cash

still a cool synth though.