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

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 :)

Hi Jim, I have a tendency to like lower impedance cartridges like the Air Tight. The lower impedance cartridges use smaller coils (shorter wire runs) usually made of gold or plated copper. The result is a lower moving mass. I think the only attribute that these cartridges have in common is a higher degree of detail and transient performance. Otherwise, they can still sound quite different from one another. You would think their tracking performance would better but I can not say I have notice a big difference. 

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.