Classical music is orchestral music wriiten arranged and recite. God help anyone who deviates from the norm. I recall Evening Standard headlines when Pavarotti sang 2 bum notes.Catastrophe.
Jazz is slightly different. While it's only about 1 /6 of the lifespan of post-Renaissance era classical it is improvised based around the head and a some times 2 chord sequence which is repeated and redeveloped often. Different veriosn of Good Bait can be done by many in all sorts of ways and they are fine.
If you want to hear a band of virtuosos operate check a Miles Davis band (the second quintet is recommended) but all his eras have considerable value.
Rock and prog rock has close relationships with classical music and the introduction of fusion (Miles is best and then his former employees McLaughlin, Zawinul, Hancock et al contribute amazing music - but Miles is the most out there and at times the most intellectual (not that that meant much in sales).
I mean this is the guy that released differant takes of So What? on 4 or 5 albums in a row. Complaints? Not me.
Structure and form versus improv. Different musics exist to achieve things some others canto or do not. Jazz is a more sophisticated blues (it's art rock arm). Classical is the art rock level of old harvest, country and folk tunes. Art rock is the musical ambition of rock, itself a fusion of roots music.
The only real difference is that only with rock can you be really crap if you are really good, or really good if you are not. (ELP versus the Sex Pistols). Imagine (if you can) all that talent and elctricity (ELP) is ... no good becuase they did not play down to a lowest common denominator. Unlike Rotten's crew. They all charged the same for their records though. Rock and roll....
Back to jazz and classical (or ELP if you want a good combo) take the rehearsal take of Coltrane's Ascension. It's much like the final take giving lie to the fairly understandable thought that these guys (Clotrane's virtuoso friends) made a bunch of noise on the spot. Not so. It was rehearsed and practiced. This and Thelonious Monk might be just why the classical world often dislikes jazz.
Then there is Duke Ellington- jazz's classical composer. Although Scott Joplin should also be mentioned in that light. Always regarded Take The A Train as the actual US national anthem. Especially after Jimi Hendrix sort of deconstructed the original. Think how that will go down at the Super Bowl, people playing that rather than singing Key's song.
Back to classical and jazz, I do improvise on themes now and then...
I recall listening to Ludwig's Aspassionata sonata once I coud have sworn I heard a brief blues lick. Was that the 13th or 7th interval in there I wondered?
To pick one genre is impossible, If the question were serious I'd be derogatory. Surely this is not so.

Anyway if you really want someone to throw a spanner in that works most effectively - ladies, gentlemen and progheads I give you Frank Zappa, the best combo of all these worlds that is not Miles Davis. And fun as well. Shame they are both dead but they have a lot of records for us to get...
P.S.
No vote but a veto.