Are we talking about the more modern Call of Duty, or the older ones? In the more recent Call of Duty games they have been geared toward the action junkie casual gamer, while Counter Strike has been geared towards the more competitive gamer since day 1.
If I had to pick a game I preferred more than the other I would pick Counter Strike since it offers a little more realism to my experience. It allows for a higher skill cap than other online titles (such as Call of Duty.)
Though that isn't to say that Call of Duty is a bad series, it's just that when I play the recently released Call of Duty 4: Modern Combat, I'm sort of taken out of the immersing effect. When after I get hit by enemy fire, my health regenerates and nothing is wrong with me after 10 seconds of waiting. You would think eventually your flesh to lead ratio would affect your life expectancy, right?
All in all, my vote goes with Counter Strike (with Call of Duty as a very close competitor.)