Redlambs
Creator of the Caftards comics
I've always associated half life with the physics puzzles and the illusion of a non linear game which in reality is very linear.
Halo's never been my thing to many bullets to kill someone so don't know the series in depth.
Well then that's your problem, you missed the best of both.
Half Life introduced us to a story driven FPS with enemies who seemed to think and protect themselves, and big open set pieces that told a story. Halo was the next (and arguably last) major AI push, with enemies who actually worked as a squad, with set pieces bigger and better than any before. Neither game were about illusions and all that, they lived and died on the gameplay innovations, AI and solid gunplay.
Halo 1 was the last big leap in terms of fps AI, I mean I'd consider F.E.A.R but that was much more corridor, and only surface. In the terms of games that pushed the genre forward, games like Goldeneye/HL/Halo/Deus Ex/System Shock have all pushed the genre on, there's no doubting that no matter if they are console or not, they are set in stone.
One thing I will say though, I'll never get the love for Halo 3. It was boring at best, only the multiplayer did anything interesting. Also, whilst I'm on it, Halo 2 broke the gunplay of 1, the dual weapons and nurfing the classic weapons was shite. Luckily the settings and atmosphere saved it.