I've got a natural skin head (calfskin maybe?) on my old Framus standard-length tenor banjo. It has a nice deep mellow sound and is loud. I use a nylon Dunlop .73 or sometimes .60 pick--harder picks bring out a brighter tone. It sounds best with strings not too old--I change mine about every 4 weeks.
I'd imagine the head (my banjo's is pretty big)would affect the sound more than the string gauge (I use .10 .14 .24 .36 or thereabouts).
I've seen some tenor banjo players pad the inside of the head with a piece of foam, like American old-time banjo players do with their five-string banjos, to deaden the sound somewhat. Another thing that affects the sound is if one plays with the little finger resting on the head, again it deadens the sound a little, depending on the pressure used.
Sully used .08 .12 .22 .37 strings on standard-length.