You know, I respect Matt Finch as an author of retro-clones, but I'm afraid his Old School Primer is only so much buncombe. Nothing about the two opposed play-styles described therein have anything at all to do with old vs. new school. To an extent, yes, he's setting up a dichotomy between using die rolls to adjudicate results and simply having the DM make a decision, but it swings a little wide of the mark to my way of thinking.
If I were running D&D 3rd edition, there would be nothing at all keeping me from allowing characters to "automatically" find secret doors and treasure troves in the event that their players described specifically how and where they search for them. Likewise, running OD&D, nothing is stopping me from handling the entire searching process with one fell Wisdom check for everybody. Neither of these things is old school or new school. They are features of the DM's play style and decision making process.
Old school and new school, rather, are things inherent to the game system; not contingent on the DM and players sitting down to play the game.
The sharpest divide between "old" and "modern" gaming is simply this: how detailed to the rules make a character? How different is one character from another in game-mechanical terms?
In an old-school game, character's aren't built; they're generated (by rolling dice), after which they grow organically along a more-or-less predetermined path. Two characters with the same class and level will look quite like each other, from a game-rules perspective, for most of the course of the game. If you strip away such variables as spells known and magical equipment, the only thing that differentiates one fighter from another, or even one magic-user from another, is how the player chooses to describe the character -- something that goes quite beyond the rules of any RPG, no matter how detailed.
Conversely, in a new school game, the order of the day is player customization and having features relevant to the game rules themselves actually representing how the player wants to describe his character. The player can arrange his stats or buy them with points, and then things like skills, feats, and powers are selected to match the player's vision of his character.
An "old school" fighter has nothing but his six ability scores and maybe a list of weapon proficiencies; if this character is to be a "gladiator" or a "knight" or a "swashbuckler", it all falls on how the player equips and describes the character. A "new school" fighter would rather have feats and such which are appropriate to the character concept, and as the player levels up, more features are built on this to further customize the character.
THAT is the heart of old vs. new school. Nothing more.
