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

Interesting question.  One would think that the low internal coil impedance group of LOMC phono cartridges would all be lightning fast and punchy, but this is definitely not always the case, not by a stretch.  Detailed, airy and open most often, yes, but sometimes a relaxed sound as well.  It just depends on the manufacturer. 

Nearly all my favorite LOMC cartridges are low impedance, typically 2-3 Ohm. Low impedance cartridges must be used with "current-injection" phono stages designed for low impedance cartridges, this combination is mind blowing. 

The problem is about ''moving mass'' on one side and ''core'
versus ''coreless'' coils on the other. Reduction of moving mass is ''obvious'' by reduction of (wire) windings on the coil former. The lower the number the lower impedance but also the output. To increase the output ''iron core'' is usually used  but has as disadvantage ''magnets saturation''. That is why ''coreless'' coils are used.
This however reduces the output which causes phono-pre problems and /or the sense of SUT's use.

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.

Also most of cheap aircores or in other words coreless coils are bass shy...

@bukanova
Very interesting comment, i blamed my phono stages because with all of them (high gain MC or MM+SUT), except just one phono stage with build-in SUTs, my Air Core FR-7fz is a bit "bass shy".

I noticed it depends mostly on phono stage, because in my situation all cartridges are "bass shy" with the same phono stages. And same cartridges have better bass definition with one phono stage i like the most.