"Sophistication" can be read in several ways. Do you mean something like "technical intricacy"?

Well, I suppose your use of the phrase "something like" would allow me to get by with a simple "yes". However, I reserve the right to ADBOC if necessary.

My choice of synonym would be "interestingness". Basically, music that, whatever its particular rhetorical, programmatic, or "emotive" features, sounds like it was written by somebody in the 140+ IQ range.

The relevant variable for me personally is subjective aesthetic response.

Surely you realize that that's just a fancy way of saying "what I care about is how much I like it." This is a step in the wrong direction: a de-reduction rather than a reduction of the concept we're trying to explicate.

I mean, obviously the same is true for me also.

Have you found contemporary composers to whom you've had as strong a positive aesthetic response as Bach or Brahms?

Yes, of course!

How do you characterize the-thing-that-Beethoven was doing?

Writing maximally interesting music.

Another way to put it would be that if a genetic twin of Beethoven were born in this era, he would with high probability grow up to be a member of the set of people I'm referring to.

At present I believe otherwise,

My curiosity is roused. What kind of musician would you predict that a modern genetic twin of Beethoven would most likely become? What predictions does your model make about the music that a modern composer would have written if he or she had been born in 1770?