OK.  First things first, a lot of people have a bad case of "Stop motion  animation syndrome" on this thread.  D&D combat runs under a weird  form of time based stop motion animation in which for simplicity  everyone takes their actions in turn even though it is actually a  confusing melee going on, with everyone trying to stay alive and kill  their enemies at the same time.  A lot of this discussion is treating  the way the rules work as if people 
genuinely took it in turns,  then froze, unable to act until their next turn.  This sort of conceit  is fun in Erfworld and is the sort of thing Order of the Stick plays  with - but it certainly isn't how my game works.  Likewise with a whole  lot of claims to objectivity.  And you don't just swing your sword once  in six seconds...
As for the same monster having different stat blocks based on the person that is looking at it, 
this showed up on my facebook feed this morning.   The same place seen and photographed from two very different angles.   And the representation is like that.  As you level your angle on  monsters changes.  The place being represented by the photo is the same -  but from different sides it looks very different.  Likewise monster  stat blocks.  In all versions of the Hill Giant stat block (if you chose  to play it that way) the hill giant is a 14' tall (or whatever)  humanoid who can smash ordinary human beings into a paste and lift an  incredible amount.  But how it is behaving is different.  For facing the  solo version it might just be the scariest monster you've ever seen.   But when you've levelled up enough to spit in Lolth's eye before casting  her back down into the abyss, it's just another giant.  Nothing to get  excited about - not even a warmup match.
And the XP for the giant  remains (approxiately) the same, whatever level it's presented as.   Whichever version used has about the same chance, but "The scariest  monster our PCs who've only been to the nearest town have ever seen" is a  whole lot more bookkeeping for the DM than "Just another giant I could  take blindfolded".
	
		
	
	
		
		
			With the Story vs. Game  question we get right to the heart of the hobby and the roots of  D&D. Is the goal of the rules to support "good" storytelling or to  place players in a defined space where they are to achieve objectives? 
The game can't support both without being two fundamentally different things.
		
		
	 
I  disagree entirely.  To be accurate one of the strong aspects of modern  game design is, as mentioned, aligning gamist impulses with  storytelling.  The better you play the game the more intense the story  will be as well as the stronger your character will be.  (And your  character will have more dumped on them because of this).
	
		
	
	
		
		
			Simulationism fails pretty hard, IMO, because  natural outcomes do not arise organically out of incomplete  simulations. A 300 page PHB is NOT going to provide a  complete enough simulation to avoid the absurd or nonsensical outcomes  arising from the compounding levels of imprecision in the rules.
		
		
	 
This.  If we ignore Erfworld, Flatland, and Order of the  Stick for a while, almost no RPGs work exactly like their rules - and  almost all of them miss out hugely important things.  But there are two  sorts of simulation - process sim and outcome sim.
A Process Sim  is a simulation that tries to take all the nitty gritty details of what  you are doing and give mechanical weight to each of them.  If you miss a  factor it doesn't happen.  3.X goes this way.  GURPS and Rolemaster both do it better.
An  Outcome Sim says that process sims are impossible to get right - and  small factors have big effects.  You're going to have to fudge.  If  you're doing a sim right then the outcomes should match up to the  expected outcomes, and you can fill in the fudge factors yourself.  This  is vastly my preferred model as process sims are IMO charging off after  something that is (a) impossible and (b) would be better done on  computer anyway with that many factors.  And 4e is a pretty good outcome  sim.
	
		
	
	
		
		
			Responding to the OP: 
First, if I'm reading GNS theory correctly (and I think I have a  reasonably coherent, if far from "completionist" understanding of it),  in my view simulationism and gamism aren't on opposite sides of the  spectrum in terms of playstyle. Gamism, as a whole, is fairly adjunct to  simulationism. A highly simulationist system can still support a  "gamist" agenda, assuming that the gamism as an agenda is at least  mildly tempered.  
Gamism as an agenda is more directly opposed to narrativism.
		
		
	 
This  is part of why I consider GNS theory poor.  I've seldom found a pure  agenda helps anyone - GNS would call an impure one incoherent.
	
	
		
		
			"Here's a challenge, let's step on up and win!"  (Gamism)
"Here's an interesting moral, ethical, or psychological dilemma, let's play out the consequences of that premise!" (Narrativism)
		
		
	 
Here's  the Kobayashi Maru.  And no, you can't hack it.  What and how much do  you save?  And how then do you come back and prevent it happening  again.  (Gamism and Narrativism together).
	
	
		
		
			Narrativist games, almost by definition, tend to devalue  gamism as an agenda, because "winning" a scene as a form of real-life  social achievement is different from "winning" or "losing" a scene to  explore the underlying moral, ethical, and psychological "matter" that  make the scene "interesting" in the first place. From a narrativist  perspective, "winning" or "losing" a scene is often equally interesting;  this is rarely the case for gamist agendas.
		
		
	 
Unless you are playing a limited term freeform (Grey Ranks, Montsegur 1244, arguably Fiasco)
	
	
		
		
			The problem D&D has always had, is it doesn't really know  "What it's simulating."  And because it doesn't really know what it's  simulating, there's no way to determine how well it's being simulated.
		
		
	 
The  word "always" is untrue.  D&D in its earliest days did.  Slightly  gritty fantasy adventure about rascals making money.  The problem was  that Dragonlance 
tried to do something else.  Something  incompatable - and from that point on D&D was trying to ride two  horses at the same time.  Neither 2e nor 3.0 knew what they were  simulating and that's why they are both poor sims.
4E is  simulating what's promised by Dragonlance and on the cover of the red  box.  And does so well.  It won't simulate the sort of environment the  Rules Cyclopaedia does - but RC D&D still exists.  
	
		
	
	
		
		
			In  other words, it means exactly the same as an at-level, standard monster  in 4E (the "same level NPC" would be an elite). The only substantive  difference I see is that 4E levels actually bear some resemblance to an  accurate gauge of the monster's capability.
		
		
	 
Indeed.  The difference between 3e Challenge Ratings and 4e Encounter Levels is simply that Encounter Levels 
work.  CR is doomed because the ability of a NPC wizard to dump everything into one encounter simply breaks the system.
	
		
	
	
		
		
			The real substantive difference is that "level" has an inconsistent meaning in 4E,
		
		
	 
[Predictable comic about overusing levels cut]
	
	
		
		
			Not  only was a level 8 monster not the equivalent of a level 8 PC, but it  could vary wildly depending on whether that "level 8" monster was a  minion or an elite or a solo. And at that point, why even have  levels?
		
		
	 
Because level is a good estimate of who it will be an interesting  challenge without too much book keeping for.  Level is one of the two  dimensions being used - but still an important one.  XP is the other.
	
		
	
	
		
		
			This design just doesn't resonate with me.  A  monster's xp value should be calculatable from its level (or HD) which  in turn defines how well it can fight; its abilities, and its  defenses...otherwise, if I invent my own monster how on earth can I work  out what it's worth in xp?  Yet here a level 8 is worth the same xp as a  level 25.  I don't get it, and likely never will. 
		 
		
	 
A level 8 
solo is worth the same xp as a level 25 
minion.  
Imagine  it as the old school random dungeons generator - they were levelled  from 1-9 IIRC.  But there wasn't always one single monster per result.   On Level 9 of the Dungeon you might roll up 1 Ancient Red Dragon or 16  Ogres lead by an Ogre Mage (or whatever - I don't know the tables). 
To  put it into almost 4e parlance, level 9 represents the dungeon level.   The 1 Ancient Red Dragon would be a solo, and the 16 Ogres would be  minions with the Ogre Mage being a Standard.
Does that make it  any easier?  Imagining that in 4e level represents the dungeon level.   The ogres are still ogres.  But an Uruk-hai seen by Sam on his own is  terrifying; one seen by Aragorn is Tuesday.
	
		
	
	
		
		
			Level (in 4E) and Challenge Rating (in 3E) are just meta-game descriptors. What the giant is - what it can actually do - must remain objective. And that's reflected in its stats - Strength, Will, attack bonus, stealth, etc.
		
		
	 
Given that 
Hit Points  aren't objective there is no way that the giant can be truly  objective.  It has to be subjective.  Objective + Subjective =  Subjective.
	
		
	
	
		
		
			Whatever else you might call them I think anyone  who has played more than a single session of Apocalypse World, Burning  Wheel, Marvel Heroic, Sorcerer or Dogs in the Vineyard could honestly  not call them games. There is a right way and a wrong way to play them,  and they absolutely punish strategic mistakes. They differ from games  like D&D in that optimal play is not reflected in your characters  having an easy time of things. There are patterns to discern and  interpret - they are just different patterns.
		
		
	 
QFT
	
		
	
	
		
		
			Yet they shouldn't be.  They, through their  characters, see only a giant; with no idea how it is represented in the  game mechanics but fully aware it's gonna flatten whatever gets in its  way.
The only person at the table to whom the giant's game mechanics should matter (or even be known) is the DM.
Lanefan
		
		
	 
On the other hand they know whether the giant is terrifying,  requiring a change of underwear (Solo) or something their expert archer  should be able to take in the eye in one shot and so comparatively slow  the expert swordsman can trivially sidestep the club and take in the  femoral artery without breaking a sweat (Minion).  They know who should be more scared of whom.
	
		
	
	
		
		
			And I will say that, AFAICT, the D&D mechanics of every edition prior to 4E have been exactly that. This given ogre has exactly AC 13 (or 7) and 3 hit points.
		
		
	 
And hit points have been very explicitely not meat and an approximation of a dozen or more things.