Overall technical competence: Half-Life 2 (or rather, Counterstrike: Source), with the Unreal Engine sequence being very close behind. I've worked with both the Source and Unreal Engines, and in short; they are widely used in the industry for a reason.
As for the best shooter GAME of all time...it doesn't exist.
Seriously. Each game I've thought of, I liked because of its flavor, and could find glaring flaws in each. Without a firm objective basis for comparison beyond technical accomplishments, comparing each work to the other is unfair.
Metroid Prime vs Tribes 2.
One is strictly single player, while the other is designed to be strictly-multiplayer.
How does Deus Ex fit into all of this? Or a Modded UT2004? System Shock 2?
I like each game because of its distinctions.
Therefore, there is no "Best FPS/Shooter Ever". I list Deus Ex as my favorite game of all time, but really, that list is partly nostalgia and hardly concrete. Analyzing older titles as an adult has changed my opinion on many of them.