Allow me to give some resons for Half life 2 as my choice.
1st -lets look at what they all have in common, (HDR lighting) all these shooters have fantasic lighting effects
ex

oom3's contrast of brightness and shadows
Halo2's reflective shine on metal (same goes for far cry and half life 2)
but I'll narow it down to 2... Halo 2 and Half life 2. I see these as the top 2 on this list one thing they both have that the frest don't is good Reflection. Halo 2 if you ever bother to look, surten wepons reflect light as well as the area around you. Half life 2 dose the same but much more clearer and almost any object (the sheen of metal and organic objects even distorts dipending on the roughness) creatures, people, the world even the water itself reflects and refracts. The floors in the game looked absolutly real its shocked me.
2-characters: although Doom3 and Halo 2 and more detailed modles they don't lipsync or move like real people. Half life 2 nails this perfectly, when someone is talking you see their lips move to each letter in the words they speak. and the whole time they do this,they face your direction no mater where you are. they even asume natural poses,
3- gameplay this is the last point...no other shooter i'v played gave you the ability to grab anything that wasn't nailed down and carry it with your gun still drawn. This added new tactics that I normaly never would have been able to do such as taking a gas barel throwing it at the enemy and then shoot at it to finish them off.