And this pertains specifically to ME... I know people who feel exactly the opposite of this.
I will always listen to most other types of Jazz than traditional... but that's because more melodic music moves me more. (an exception coming up). Traditional jazz, again, for me, has a more mathematical presentation. It's not 'emotion' that I mostly get from it... but rather a sense of 'awe' in how amazing it is... like pondering E=MC
2The exception... I have not attended many traditional jazz concerts... not by choice but rather the fact that very, VERY, few have ever been held in my area... at least by noted traditional Jazz stars. (mostly college bands, which are quite good). So I have very limited experience in the type of venue you mention... BUT.. i have been to a few... and that changes everything for me. When I am among those who can truly 'hear' the sophistication of traditional jazz there is a 'bond' that forms.. a sharing with the other people in attendance, and that IS emotional... and frankly every bit as enjoyable, in that circumstance, as the more melodic types of jazz.
With that said, however, there are many songs in traditional jazz that I just don't get. Some by Coltrane, and Davis, (mentioned because they are most noted). Some of them I have listened to time and time again trying to 'find it'... and have failed. Occasionally I'll catch on... but the effort it takes muffles my enjoyment.
There is definitely a sense of accomplishment, however.