The head bit is purely a matter of taste although real hide is more sensative to changes in temperature and humidity. As a rough guide, "plastic" = sharper, brighter, louder; hide and "synthetic hide - fyberskin" = mellower, quieter. The only place I can think of where there are sort of "rules" is with the 5 string banjo. A bluegrass player is likely to use a different banjo and setup (including the plastic head) to an old time player to get the sounds they want.

ieng pedantic, barry is wrong in calling a plectrum banjo a type of tenor banjo neck. The plectrum banjo was a 5 string banjo with the 5th string removed (and changes to the neck to make it a 4 string instrument). The tenor banjo was a later effort to make shorter scale instruments.

Valuation of tenor banjos probably vary a lot from country to country. In the UK, a tenor (19 or 17 fret) probably has sort of equal popularity with the 5 string. I believe that in the us 5 strings are dominant and good tenors are often looked upon as candidates for conversion to 5 strings.