It's all about feedback and goals :-).
It's easy to put a few 3D models in a simple 3D world and use a gun to kill them. But how the world+models react to your actions is what makes the game fun. And killing the baddies is never the reason to play (or else all those "one box with 1000 monsters" type of custom levels would be fun).
Personally i love the oldschool FPS games, but only those who got feedback and goals right.
What i mean about feedback depends on the FPS game. It doesn't have to be serious (Duke Nukem 3D rules and is far from serious) or have detailed HDR graphics (or else people wouldn't still play them - and i'm talking about *new* people who were not around the days of Doom).
In games like Doom, DN3D, Quake, Painkiller, Sam, etc you are the uberstrong megahero who can save the earth (or his ass, depending ion the theme). The guy who faces hell, beats its demons and comes out alive. It may be unrealistic (as probably opposed to all those "you are a mere soldier like other thousands" FPS games), but many people play games to escape from reality. And many people would love to be such "gods among men" (as said in FEAR's introduction - BTW i consider FEAR to have more oldschool gameplay than many other FPS games).
However, such heroes cannot be only described in the game's manual. The game itself has to convince the player that he is actually capable of what the manual/story says. And this is done by feedback. Feedback from the user's avatar, feedback from the user's actions, feedback from the world itself.
To provide good feedback you have to leverage what is already known to the player.
The user's avatar cannot be a wimpy guy. While technically he *can* be both wimpy and uberstrong, Movies and action comics teaches us that strong guys are beefy and muscular (usually with extra muscles a normal human won't have, but we're not talking about normal men here). So the avatar has to follow these guidelines or most players will feel that their avatar is "lame".
Note of caution: many people will react to this by pointing at Half-Life's Gordon Freeman who is supposed to be a noob physicist, unrelated to any kind of action (before the accident) and wears rectangular glasses (notice how nerdy GF's glasses are - anyone knows, from movies experience, that cool glasses are mostly curvic
like these and the glasses we saw Vin Diesel to wear in his movies - except
these). Well, it's true but this image is quickly forgotten when he gets his first weapon - a crowbar (a
melee weapon which he uses with ease - so the guy actually has muscles), and later some guns which he uses without problem. Besides, while other scientists are screaming around, he remains silent but instead goes to do something (cool guys act don't talk, and all that stuff). So basically, Gordon Freeman *is* a superhero somewhat, but when Half-Life 1 begins, he just don't know it yet.
But the avatar alone is not enough. Ok, you're an uberman but what's cool about it if you can't prove it? The environment must react to the players actions. Duke Nukem 3D was notorious for the environmental feedback - breakable glasses and items, holes from bullets, many ways for monsters to die, etc. In Doom the doors were *massive*, with bassy "strong" sounds. In Quake the whole world was made of solid rock and metal. Even your weapons - a double shotgun, a nailgun, an axe, etc - were made of the same material and their sound was strong.
In Blood and Quake, when you killed an enemy, pieces of his body would fly around. Now, many will focus on this being the reason for these games to considered from some as good games. However this is not the case. The "gibbing" itself is not what made the games good, but the idea behind gibbing - a strong feedback to the user's action. Of course since the game is all about shooting, and shooting mostly destroys stuff, gibbing the enemies is a strong feedback. And breaking stuff, like in Duke Nukem 3D, is also strong feedback.
But don't be fooled with reality and think that this is true because "that's what would happen in reality"! If those flying brains in Duke Nukem 3D instead of falling down in a bloody mess, disappeared into a strange plasma-ish cloud (assume for a bit that this was possible back then) with a wave effect of a moment that affected the whole screen (much like those explosions in Doom 3), the feedback would be as strong - or stronger.
Feedback doesn't only come from the actions, but from the world itself. Presentation is an important thing, especially in FPS games where you try to immerse the player in your world. Note that "presentation" doesn't mean "high tech graphics". Don't make that mistake. Good presentation means a coherent world where the player's character and goals fits in.
Many partial game mods or even official expansions can show this. Take Unreal 1's expansion for example. This expansion breaks almost everything i said above (like using a totally nerdy voice for the avatar between levels). But here i'll talk about the new weapons and monsters it introduced: both of them seem out of place. While the original game's weapons were all "alien" (in the sense that they weren't very familiar, like those in Doom) and designed like alien, the new weapons were more realistic and their design was too "human like". Granted, they were supposed to be designed by humans, *but* the default weapon was supposed to be designed by humans too! No, the real issue was that the art style (presentation) was different - ie. not coherent with the original game. And the monsters were similar too. Some reviewers bashed spiders for being too common. But you know, that wasn't the problem. Doom3 had spiders too, but their design was fitting in the game and besides they were one of the good monsters in the game. The problem was that these monsters were nowhere in the first game, while they were all over the place in the expansion, so breaking the game's coherence *and* that their design didn't match the design of the other monsters.
Presentation doesn't cover only appearance, but also animation and sound. Some amateur models can show the problem with animation: most characters (and monsters) have silly walking or attacking animations, which makes the whole game look silly and thus breaks the immersion. See how "determined" the walking and running animations in Quake and Quake 2 are! And notice that the monsters do stop attacking you while you attack them if the blow is big (Ogres fall down, soldiers become a bit dizzy, etc). Also another problem is sound: some sounds simply doesn't fit. And this is a usual problem with weapons. In Doom3, for example, the machine gun's sound is a joke. Compare it, to the sound (and aural feedback!) of Quake 1's nailgun, and you'll wonder how both come from the same people. Not to mention the silly sound of Stroggs in Quake 4...
But weapon design is a whole area itself. Technically hitting a monster with an axe or a broom is the same thing (in fact the broom can cause more damage just by increasing it's "damage" value). And sound is not the only problem here: the weapon has to be convincing not only on the looks and the sound, but also on the behavior. Unreal 1's "8ball" weapon is a nice example of this: the weapon looks devastating, the sound is supreme especially if you fill it! But the damage is minimal and the load time is slow. The first comes against the weapon's look and feel - eight rockets must do a huge deal of damage! Heck, on
other games one rocket is enough to kill two monsters, while 8ball needs to be full in order to achieve the same thing! And the game itself doesn't help it either, since it presents it as the "gun of gods". The gun was supposed to be (because it was presented like that) the gun that would eliminate all Skaarj scum from the planet. Well, ok, but the problem is, in the time it takes to load the gun (so a Skaarj can actually die from it), the player already has been hit a couple of times (Skaarj doesn't wait) and when you finally release the rockets, the Skaarj side jumps and avoids them.
Many games got these wrong. It is also the reason that in 90s people were "bored of generic FPS games looking and behaving the same", yet the FPS games which were playing were doing the same thing, but did most things right. FPS games were (and still are, however not as much) a hot genre, so anyone made their own Doom/Quake/Whatever_popular clone, usually getting thing wrong. So players saw these clones, saw that the intention was to make a doom/quake/?? clone, saw that the gameplay was bad and decided that " generic fps are bad". But that's another story :-).
Whatever i said above, i think it applies to most FPS games. What makes *oldschool* games entertaining is the level design - or the "goal" i mentioned above (note that here when i say "level design" i don't mean the architecture of a level or how items are placed in it, but the whole design and behavior of the game when focusing on levels). Doom, Quake and Duke Nukem 3D doesn't have much of a story to tell and their mechanics are really simple. So what they have to show is pure gameplay. Some said that Doom (and Quake and DN3D) is all about finding cards and opening door. Well, this is mostly true and it's the backbone of the gameplay, but like a living being, it cannot rely only on the backbone (for most living beings anyway).
Doom's (and Quake's) level design was all about making you feel unsafe. You have an area cleared, go forward, kill some baddies, pickup a key, come back and there are new monsters. Some monsters are "deaf" - that is, won't hear your gunshots but they will attack you *if* they see you. These are good for traps (remember the cases where you killed everything in sight only to be killed by that monster which was hiding behind those boxes?).
Duke Nukem 3D's design is more "in your face", sporting more action and less traps. In Duke Nukem 3D the designers' goal was to put a lot of action. Duke was more equivalent to an action movie than a horror movie.
Serious Sam draws more from Duke Nukem 3D than Doom. In Serious Sam, the goal of the designer is to put as much
brainless (=simple) action as possible. Unlike Duke, there is no major theme to drive the game. Everything is about gameplay only.
Painkiller, is like a serious "Serious Sam" :-) with some bits of Doom added.
While all these games may look the same from a gameplay perspective, in reality if you see the details, they're different. What makes them look the same, however, is their design choice of focusing on simple gameplay elements and goals (horror and/or action) and that the level design is made with these elements as the primary goal of the level. This comes in contrast to some other FPS games (or other games in general) where the primary goal is to have a realistic environment where the gameplay has to wrap itself around it.
These games' designers have a different goal, which usually is to produce a realistic experience. Some may like it, some may not. But this is a different discussion (personally i prefer gameplay-oriented FPS games).