Given that it was originally written as a descant solo for piccolo in a marching band context, one might think that it was the easiest to play it on. Alphonse Picou's adaption of it for clarinet - on which it became the acid test for aspiring New Orleans clarinetists - showed that it was not easy even on a mobile instrument like the clarinet. I have a recording of Picou playing it with Kid Rena's band in 1940 (the only time he recorded it?) and while he was admittedly past his prime, he does struggle for breath at one point. Actually as a marching band piece, it's not that fast, just tricky.
Bechet ripped through it on soprano with ease and varied the phrasing slightly. I expect he could have done the same on clarinet with equal facility.
Charlie Parker famously quoted from it during his solo on Koko, to the extent that some people think that's where it originated. He tosses it in so quickly,at breakneck speed, that it's almost an un-noticeable phrase amongst everything else. Again, I suspect he could have gone through the whole piece with ease if he had a mind to. He probably had done during his woodshedding period, which is why the fragment came so easily to him in a solo.
Lots of others have used it on different instruments. I heard a fragment during last Saturday's BBC Radio 3 Jazz Record Requests in (I believe) a Stan Getz solo on Shine. I even remember Malcolm, Bari123, quoting a run from it in a solo at Karen Sharp's workshop a few years back.
While it may be easier to play on a physically smaller, more responsive, instrument, I think in the end it depends on the individual player's fingering facility and to some extent, endurance to play it right through at required speed. Why, are you thinking of doing it on the EWI?
I found a 1959 version by Alphonse Picou (two years before he died) from a TV show on Youtube. http://www.youtube.com/watch?v=8yl28cD3YZo He misses out a few notes from the original - hardly surprising given his age - but it gives a good idea of what it was like. The banjo player looks like Laurence Marrero so it might have been with George Lewis' band.
Just to resurrect this thread and show the ubiquity of the High Society break.....Christmas presents from my family included American Ruby Braff's (a cornetist for those who don't know...yes, I know this is a sax forum) last concert, in UK at the Nairn jazz festival in 1992. On a crackling version of the old standard Dinah, Braff's guitarist Jon Wheatley throws in the oft quoted run from High Society. Yet another instrument that it has been played on. Actually I think I've heard Joe Pass play it too.
There are two more things about this cd that help make it really good. One is that Braff's front line partner is tenor player Scott Hamilton. He's a fairly recent discovery for me. Very lyrical and always swinging. I saw him last year at Dorking jazz club in Surrey and he didn't disappoint. The other is that the drummer and bass are Steve Brown and Dave Green. They are part of Karen Sharp's quartet and appear with her on her album Spirit released late last year.