An excellent primer on the differences on how the rules drive D&D in the original edition, referred to a 0e, and modern editions (3e/4e) can be found here [pdf].  While I have never played 0e or 1e, it’s been such a long while since I played 2e that I had forgotten how much the way the game is run has changed.  

Modern editions of the system don’t restrict players and dungeon masters from playing modern editions the same way they did with older editions.  However, they do focus on the abilities of players’ characters through mechanical rules as opposed to leaving more to the imagination of the players and the DM.  This creates more opportunities for players to slip into mechanical “rollplaying” instead of encouraging “roleplaying”.  With the right DM and players, of course, even modern systems with its abundance of rules can come out feeling like old school!