I am late to the party, so I hope I don't repeat to much.
While
Challenge the Players, Not the Characters' Stats sounds neat and catchy, I think it doesn't really help us.
Particularly, I do not think a skill system is at odds with this.
If you wanted to challenge the character stats in an RPG, you just would set high DCs. But that is not what we do in any game.
In a way, you always create various "puzzles" the players have to solve with the tools given to them. Sometimes, that's really just their ability to solve a word-riddle, and has no bearing to character statistics. Other "puzzles" can be the mini-game of optimizing a character, or coordinating the party to use the optimal combination of attack powers and tactical positioning to defeat their fictional opposition.
I think the "old school" approach is not really defined by the idea that you challenge the player, it is more defined by the fact that you focus on more "direct" puzzles. Stuff like "which lever to pull" or a word-puzzle, but also by hearing the NPCs words and discover the lies in his words.
"New School" doesn't encourage this as much, since the desire is to role-play a fictional character whose mental abilities, skill-set and even personality might differ from that of the playing character.
If you want to play a character really different from you, you can't just rely on your own abilities.
That's why we use mental ability scores and skills, but also spells. So the nature of the puzzles change, involving the new sub-systems. A very simple example: You don't have to know which lever to pull, but if your party has no one with the Thievery Skill, maybe the Wizard player should remember that he has a wizard spell (or a ritual) that might help him here.
Many RPGs contain a certain degree of "resource management" that is a puzzle in its own right. D&D (even "old school") always had its spells for most of this. Many classical D&D spells are "game-breakers" because they solve a puzzle. A simple spell like
Detect Evil can make an investigation a lot easier, while a
Knock spell avoids solving the "find the right key"-puzzle, and a
Find the Path can avoid all that little and large legwork required to get to your intended location. But while you avoid the "classic puzzle", you get a new one - which spells do you prepare today? Do you cast this spell now, risking that you need it later?
Still, in any case, both old and new games work best if you still challenge the players. You might give their PCs skills, spells, feats or powers, but in the end, they are just tools the player has to use.
The only case where we really get into a "callenge the stats" scenario is if the player would not make any decisions, and just roll dice. It is possible to get there - imagine a 3E or 4E like combat system that abstracts movement and positioning and replaces it with a "Tactics" skill roll - and remove all spells, powers and combat options. Suddenly it's a game of luck and statistics. But even then, there might be a hint of "challenge the player" - if the player could build that character on his own, "system mastery" might help him to select those options that work best.
I think these extremes show one thing what people like about "old-school" - you are "closer to the action". It's not enough to make a stealth check to hide. You need to describe where and how you want to hide. "I turn the lamp so that it blinds anyone entering the room, and hide behind the door." This feels a lot closer to the game world then "I roll 24 on Stealth. I am wearing an Elven Cloak, so as long as I have concealment and don't attack or move, I stay invisible, so even if he beats my roll, he can only hear me, and I use my daily "Ninjas Hiding" power so I can reroll my first failed check."
What people like is entirely a personal preference. I can see the appeal of "old school gaming", but I am more in the "new school" faction where I want to solve the puzzle of using the right character abilities, since I want to have the feeling of being someone else then me. And if it is me to pull levers or come up with a clever ghilie suit in swamp instead of my character, I don't feel like that.
