Jazz isn't about intensity or aggression, and while technique is important I don't believe jazz can be boiled down to it. Jazz is comprised of two things:

Let's examine where Miles, Coltrane, Sonny, Jelly Roll Morton, et al really came into their own. While every single one of these gentlemen were or are fantastic instrumentalists, they are known for variations on themes already established (Someday My Prince Will Come, Greensleeves), experimentations in structure (Kind Of Blue, A Love Supreme) and then the experimentations which featured the total disregard of structure (Ravi Shankar, anything from Miles' last five years.)

It is of my opinion (which while practiced, educated and experienced is just an opinion and should be taken as such) that jazz is about structure, the same way classical music is, at its very foundation, about structure. As such, I do not believe that what we call hard core is the new jazz.

While Soundgarden may use time signatures that aren't divisible by two, that hardly constitutes them being super-complex. Complex meters and figures and the ability to perform them does not delineate an artist as a genre unto themselves, nor does it necessarily lend validation to the product. Rage is aggressive but they aren't really doing anything new or reshaping an old form. Lyrics are important to all good songwriting but words with deep meaning should hardly be associated with jazz; take a look at most jazz lyrics and you'll discover very little introspection. It happens, but its rare.

There has been an influx of excellent music which almost entirely owes its roots to either jazz or classical, and its what I like to call symphonic rock and roll. Radiohead and Tool are both in this group, and they earned their places there:
  • Radiohead is constantly utilizing forms, meters and modulations which positively reek of classical music. Paranoid Android is a perfect example: It has the classic A-B-A2 sonata form, with A2 being the fully developed line of A and B acting (both structurally and modally) as the development. Treefingers features modal composition. Anyone Can Play Guitar features both canonic motion and chromatic tendency.
  • Tool is once again a classical structure bandit. Sober is built on a jazz structure. (A-B-A-B-C-B-A) Each Tool album could be categorized as a song cycle. Aenima features all the elements of a symphony but in a single movement. Of course, A Perfect Circle is quite similar.

It's also important to remember that these are not the only examples of symphonic rock but the ones I have off the top of my head.

In conclusion, the "new jazz" or "new classical" will be music approached from a compositional standpoint with thought given to structure, harmonic progression, and development.