Um... Are you asking which ones we like or are you just saying that you like strategy and shooting games? Since I don't know at all, I will just assume that you want my opinion.
Strategy games, require use of intellect and strategic skill. Shooting games, require fast reflexes, good awareness and good skill at controlling your mouse/keyboard/controller etc.
I prefer strategy over shooters to quite an extent, especially RTS. I still play shooters, since I enjoy playing fast paced, action oriented games.