Same answer to both questions: Q3 for 1v1 and CS 1.6 for 5v5.
Both have an extremely high skill ceiling, whilst still being very popular amongst different levels of players. This allowed for both high quality play at the top level as well as significant prize pools and tournament sizes. They also have no-frills high performance engines, as well as map, gameplay and effects design that allowed for minimization of the random element whilst still having enough variety to be interesting to watch. I don’t think anything has been released since then that can compete on the same level, although I guess CS:GO is reasonably close to 1.6 in quality and has taken over the tournament scene.
If the question was “which competitive shooter did you enjoy the most”, then my answer would be something entirely different: I’ve played the Half-Life mod Natural Selection, and its standalone sequel, competitively for about ten years in total, with a significant amount of success. Both games suffered from fairly convoluted, unique and complex gameplay design, as well a high skill floor – which was further compounded by an increasingly veteran community – which led to limited popularity and all that follows with that. The sequel also suffered from having a poorly performing engine, as well as map, gameplay and effects design that suffered from a high degree of visual and aural clutter. Both lacked persistant progression, which is a very important factor for gamers these days.
I’m not sure if it’s possible to quantify exactly which factors make a great competitive game or not, but I personally feel that popularity has to be an important consideration. Competitive gameplay quality is also important, but tournament size will never reach a large enough level to start the ball rolling for truly professional play if the game lacks the necessary playerbase to support it. Most of the games mentioned in this thread so far had the requisite competitive gameplay quality, but they lacked popularity.