Nice question, alhough a bit 'generalistic'. Anyway, here I go:

Orthodox/Classical: mostly active / aggressive and, if White chooses so, positional
Taimanov/Kan: mostly positional
Sveschnikov/Kalashnikov: quite active / not necessarily solid, but sound
Pure Najdorf: active / aggressive and, if White chooses so, positional
Dragon: active / aggressive and, if White chooses so, positional
Pure Schevinengen: active / aggressive
Schevinengen with Najdorf move order: active / aggressive  
Accelerated Dragon: mostly positional and quite solid

And don't forget of the 'bl$$dy' Anti-Sicilians