High vs low internal impedance cartridges....Is there a sonic signature for each type?

Coreless coil the most known example is Denon DL304

and if to speak about mainstream flagman AT-ART1000

Although it’s important to define what does it mean low ohm - to me it’s up to 5 ohms...
in most old SUT’s it’s marked the same, most of them "low " means up to 3 ohms like mine FR XF-1 type L

The more wire you'll wind the more signal you'll get and impedance will rise. 
Although there is much more between ohms - magnet type/size/form, wire diameter, winding technique, core material (permandur, iron, aircore), size of magnetic gap etc.
So it's better just look only into fingertip - stylus. Life is easier :)

air core is bass shy by nature although masters found the ways to compensate that. Ikeda used plastic cube to wind a coils in order to get more homogenous magnetic field and more bass. Friend of mine changed permanent magnets into field coil only due to lack of bass in his air core designs. Aircore isn't the design which is intended to be bass heavy although you can hear bass details  in the music.

magnets also differs - the most sweet one is alnico, the intermediate is samarium cobalt, the strongest one is neodymium. 
Although if you will look into the picture core moves in magnetic field made by permanent magnet (or field coil but that one is exotic) and less turns makes output more homogenous  but signal/noise factor takes over.  Also most of cheap aircores or in other words coreless coils are bass shy...
But IMO if you will look into core of the problem why we do like old designs fastest/easiest answer is the use of neodymium magnet in cartridge designs from big manufacturers like AT, Ortofon, ZYX, Lyra etc.