Technically Good Jazz
This would be your Tubby Hayes's and (early) John Coltrane's of the world. Every note is played. Their technical ability on their instruments shine through as they play nonuplets at 200bpm; while their harmonies and phrasing are perfectly precise.
Unfortunately for these greats they leave many-a-jazz listener in the dust as they blaze a trail to the nth modulation of C#-7flat5 13. And there is a fine line between knowing what you're doing here, and doing what I call "Typewriter playing" (flying your fingers round the sax with little direction so fast that no-one can really hear what you're playing)
So hear we have immense skill, but only for those worthy enough to be able to hear it; many of the intricate and delicate harmonies being hidden away in hemi-demi-semi-quavers. I remember when I was younger I would listen to these guys and leave with a headache. But I kept going back, because every time I did a new harmony was un-earthed, a new level to their solo was unlocked.
I could listen to the same piece, Giant Steps for example, for 10 years straight and still find new things to enjoy and hear about it. I know this because I have!
Now this would be every band that lays down a dorian minor chord and plays vertical solos relying on one or two sweet notes or blue tones.
The solos are long, as are the notes within. Often with overtones, large variations in pitch and often sticking to one night a playing it over and over.
There is nothing to miss here. And often I find there is nothing here. The pace is so slow I often find myself thinking "Are they really amazing and playing the subtlest of intervals...or are they just shit?"
When this music is played right it provides you a window into the soloists soul. You really can feel their music and connect to the musician. This accessibility is largely why it is popular.
This is the kind of music you would want to relax to, however. Something you'd smoke a pipe to, or perhaps some other shag. Whilst relaxing in a big chair; surveying the bustle of London. Like a big pretentious nob.
Now I think there are some real gems in this genre, and some absolutely fantastic musicians who can spin a whole story in just 3 notes (Think Miles Davis) but the nature of the beast allows far too many talentless pretenders to have a go, because at it's core this jazz is easy.
Earning a Crust Jazz
This is the jazz all musicians hate to play. Its your straight blueses, your Autumn Leaves your long winded vocal numbers from 1920 and your Oh When The Saints!
But, this is the music that we all get asked to play. Ten times more often than any other type.
We don't really mind playing this music, but jazz is about the pursuit of new sounds; new feelings, new rhythms, harmonies, intervals and melodies. So re-visiting the same tired 2-5-1's every week quickly becomes tiresome.
And the thing we hate the most about this music. Is that sometimes, we enjoy it. You'll find yourself singing along, tapping your foot and enjoying your wanky 12 bar blues solo comprised entirely from the pentatonic minor! Then after you will feel dirty, and ashamed. You see this kind of jazz is like a riding a mo-ped; great fun while you're on it, but you'd never want your friends to know about it.
Someone's experience of jazz is entirely subjective, this is why there will never be a definitive answer. I find the technical jazz exhilarating and exciting - others find it to be an exercise in mathematics and showing off how big your nob is.
Jazz comes down to a listeners experience. If they enjoy it, and get value from the music be it by a connection the the musician or music itself or by an intellectual gratification of the music or simply by hearing a tune you know and love; then it is good jazz!