I can hear the difference as you describe EXCEPT for my tastes the TI sounds more musical. I much prefer the sound of the TI in your examples. They are bright out of the box and take a few weeks to settle down and then once broken in they hold that tone for years and years.
Jazz flats are quite bright when new - that rolls off after a month or so. They are definitely mid forward and a little lacking in bass fundamental, but you can counter that to an extent with EQ. You might also like to try Dunlop stainless steel flatwounds which are somewhere between the EB Group 5s and Jazz Flats in both tension and tone. I have also had great results on fretless with Thomastik Jazz Roundwound strings and La Bella black nylon tapewounds. Very different sounds as you might expect, but characterful and comfortable to play.
The TIs get much better after you've played them a few weeks. That clickiness and sharpness goes away. Then they pretty much last forever. I don't think they'll get as fat sounding as the Ernie Balls.
