Honestly I think Doom is where it came together the best, Quake was technically better (of course) but it was not a better game.
Although, to be fair, we played Doom over an RS-232 cable - hauling a PC across the city every weekend was a testament to our love for the game :)
The campaign has a place in my heart too, even if it's not perfect. A lot of DOOM's level design was predicated on claustrophobic interiors, and when you go "outside" in many levels it feels like a glorified courtyard. From the very first level, Quake 2 pushes hard to create an illusion of environmental complexity that plays very distinct from Quake 1 or DOOM.
HL1 took both the engine and the genre further + continued the modding culture that brough Counter strike and other mods
(Note I know very well that Half life is not an ID software game, it only took the engine that was auper heavily modified / updated- but it my opinion this is the successor)
Each had standout maps that made you want to own both, such as Q3A's Longest Yard and UT's Facing Worlds. I ended up playing more hours of UT because I had slow internet and its bots were better.
Point being: Q3A was great, but in 1999 it became clear that id Software had lost their head start over other FPS developers. They were still elite, but in the early-mid 90s they were alone at the top.
https://www.gamespot.com/reviews/quake-iii-arena-review/1900...
https://www.gamespot.com/reviews/unreal-tournament-review/19...
https://thelongestyard.link/q3a-demo/ (instant, even works on phones)
https://dos.zone/mp/?lobby=ut (scroll down and click Create on CTF-FACE)
They even have multiplayer support.
I hope someone ports UT2K4 someday so I can play ONS-Torlan.
As for id drama, there was plenty after Quake 3. I remember a .plan update from John where he talked about people leaving and people getting fired...I think one of them was John Steed (rest in peace), one of the player modelers who was very active in the modeling community and well liked. Felt like a disaster at the time. I just think there was a lot of conflicting personalities at the company and it was doomed to fail (no pun intended).
I think the point is that Quake (1) came out within months of Activision launching Mech Warrior 2, Blizzard doing Warcraft, and even a couple years before Valve did Half Life. And Quake / Doom were so much bigger.
They had terrific success but if you were handicapping US video game companies in 1995 it would be like EA, iD (and maybe Sierra Online!). Point is they were way ahead at that point.
It's not that the company was ruined, but that it had lost some of its creative direction after Romero left (while retaining technical excellence).
Not just graphics but character acting and animation, interactive world elements, deliberately dramatic scenarios in the levels (Half Life pioneered this, but Doom3 had a lot of really good ones).
It was years ahead of what was on consoles at the time.
https://www.youtube.com/watch?v=aTJ1weGimZQ
and
https://www.youtube.com/watch?v=y_3vMUOayyc
Doom 3's fully real time lighting and bump mapping was technically impressive, and the live interacting UI was very trick, but the character acting and animation was definitely not SOTA. That was Half Life 2. And if we consider impact on the gaming landscape, Doom 3 was if anything a dud. Elements from that game were not taken along, including not even in subsequent Doom games. Meanwhile Half Life 2's approach to storytelling & world building, animations, physics system - those practically defined the next generation.
In general while Doom 3 has the better (and probably more forward thinking) rendering tech, HL2 also had some very good tech for its time and did a much better use of the tech they had available than Doom 3 did.
That said, personally i enjoy playing Doom 3 much more than HL2 but that is largely because Doom 3 plays more like a traditional shooter with very little scripting / storytelling to get in your way (and the little there is you can ignore it without losing anything) - you just shoot demons, find keycards/PDAs to open doors and that's it for the most part. I often just put it in low volume and play some podcast in the background :-P.
As for Far Cry, the game looked too plastic IMO, i remember playing the game and the characters' muscles had specular reflections :-P.
Quake and Quake III Arena was were the magic happened.