Here are just a few of the reasons many people have offered for preferring the results of "old school" design, and some corresponding design elements
Thank you for some insight as to why "system matters". Cutting through the signal:Noise ratio, it helps define the terms we have been firing back and forth and gives us some examples.
Allow me to give the "new schoolers" manifesto.
Preference: Cinematic Combat. Elements: The ability to incorporate movement, strategy, unique combat maneuvers, and other drama-inducing elements into cut-and-dry combat.
Preference: Balanced Game. Elements: No character overshadowing another; meaningful choices at all stages of game. Guidelines for appropriate balance in encounters and treasure.
Preference: Non-Combat Task Resolution System. Elements: some meaningfully defined skill system complex enough to allow diversity of character choice, simple enough to allow the DM to ad-lib when needed.
Preference: Character Lifespan. Elements: Ways to create complex PCs at the starting point and play them (with luck and skill) throughout the course of the game. Removal of "cheap shots" that bypass character defenses. Abilities that make combat "fair contest" and don't allow the PCs (or the DM) to bully through a long-played character with only 1-2 dice rolls or reduce a spectacular end-game scenario to a non-encounter.
Preference: Unified Mechanics. Elements: Game mechanics using similar task-resolution systems, removal of sub-systems (esp class-related subsystems) that slow down play.
Preference: Expanded Fantasy. Elements: An incorporation of modern trends in fantasy coming from a variety of sources (novels, games, movies, TV) in both fluff, mechanics, and artwork.
Preference: Smooth Play Experience. Elements: A game that is simple to learn, hard to master. Enough rules to create a unified "game experience" without straight-jacketing a DM to one play style alone. New game elements that build off older ones, not supersede them.
Note: Some of these elements are available in Old School games as well, and not all New school games meet these marks. However, these are the elements I think that define new school game experiences.