JBL 4349 or Klipsch Cornwall IV

I always thought that the JBL 100 was great for rock but not so great for classical, the reverse of what you write. As for the Cornwalls, according to the reviews I've read and heard, in addition to the views of audio sales people I spoke with, they are less than ideal for classical, better suited for rock and le jazz.

Thanks for all the input so far! 
I do understand that the Cornwall IVs are more critical when it comes to amplifier matching, given that my current amps are a Mark Levinson 432 and a “spare” Bryson 4B-SST, my setup is likely a much better fit for the JBLs. It does however seem that there are good amps suitable for Cornwall IVs that are relatively inexpensive. The question is though if a Mark Levinson amp, albeit seriously overpowered for high efficiency speakers, is a poor match with Cornwall IVs? 

Cornwall IV seems like a good match for me, the fact that there’s not a lot of really deep bass is no concern, it might even make it easier to integrate the speakers in my room. On the other hand, what I enjoyed about L100 classic was the physical impact they had, not sure if the Cornwall IVs will give that (although L100 classic don’t have deep bass either). I’m not really looking for a forgiving speaker, too many forgiving speakers are just plain dull even with the best material. On the other hand, there are revealing speakers that sound really good with a few recordings in a certain genre. It seems though that Cornwall IVs manage the balance nicely judging from your input above. 
As there’s no way I can demo Cornwall IVs at the moment I’ve come to the conclusion that I will accept the offer to try the 4349 in my home, if I like them, they stay. If I don’t like them (maybe too much mid bass or whatever), based on reviews and valuable input above, I feel confident enough to buy Cornwall IVs unheard. In this case I can start with the Mark Levinson amp and upgrade later. 

Well, for low volume listening I think you can't get much better than the Cornwall.  It sounds full and rich at low volumes.  The Cornwall sounds really great with low powered tube amps but your current amp will also work fine as well.

I own L100's and love them. They replaced a pair of Cornscalas which for my listening area were just too damn big. Can't really say anything about the Cornwall IV or the JBL 4349 but I have owned Heresy II before and the L100's hammer out Classic Rock, Blues and Metal beautifully.

@quad78 I enjoyed them with classical music mainly because of the scale and the lack of midrange warmth. Not sure if they were tonally correct but they were great fun. In my room they imaged surprisingly well and they had an open character that worked well with string sections (with some speakers you can’t tell if there is one violin or if there are 20) and choruses (I had these right before Christmas and enjoyed an old recording of Christmas carols with the Choir of King’s College, Cambridge). Jazz was also great fun (trumpet, saxophones) with L100.  They also managed very well with the complex Afro-bossa (Duke Ellington), my studio monitors (Genelec 8050) and my Dynaudio Confidence 20’s are not even close. 
With rock they were great with some recordings  (Deep Purple’s Smoke on the water was amazing for instance). I don’t think they were very engaging at lower volumes though, they need to be played loud to be really fun. The problem is that some records contain a lot of treble energy and that’s why I had problems with L100, playing loud the treble was too much for my ears occasionally. It’s not often I have experienced listening fatigue but I did with L100. This may be due to a combination of the speaker, my room (large window on the right side wall) and the volume. In another room they may perform differently. 
In addition, with Billy Joe Armstrong’s cover of Kids in America, they did not portray the rhythm as well as my smaller speakers. I did not think the speakers were great with Bruce Springsteen’s Western Stars, my monitors do a better job with that album. 
AC/DC (Back in black) is one example of where L100 were very exciting when played loud but in the long run caused fatigue.  
But again, impressions are based on auditioning them in my room (which of course is great), another room may interact differently with the speakers.