Its the second time I'm buying Jazzicato Tungsten. Had them a couple of years ago, and after some time with steel strings on I found some old recording of myself with Jazzicato and instantly started missing the tone.
The jazzicato tone reminds of old jazz recordings (like mr Paul Chambers) and I really love it - it's mellow, dark, feels a bit gluey. I especially like d and g strings without steel's brightness.
What is also nice is tension - they're low tension, easy on hands (what I like is I can have action pretty high without struggling. It makes Jazzicato great strings for walking lines).
Even though they have only metal core they work great with magnetic pickup (Schaller).
They are also bowable at basic level (enough for some basic bow practice)
Cons: volume is noticably lower than steel strings (well, it's not an obvious con, depends on person), life is shorter (yet the price is lower). The lowest notes seem maybe a bit blunt and it's a bit harder to make them sound present than on steel strings (but I guess it's subjective).
I'm pretty sure it's not the last set of jazzicatos I'm getting :)