Let's define some terms:
Imagine you're playing a Western genre game, and two players walk out into the street for a gunfight. A Task Resolution game would handle this by having the players roll the dice to determine whether or not individual shots hit, and how much damage is done by each bullet. Eventually one character or the other runs out of hit points, and that's how you tell who wins.
A Conflict Resolution system, on the other hand, uses the dice to determine, more or less up front, who walks away and who dies in the dust. Details about how much damage the winner takes, whether or not bystanders are shot, and if our winner has any bullets left when the loser's friends come out of the saloon are determined by (for instance) comparing the players' rolls. No real effort is given to individual shots or tactical maneuvers.
D&D is a task resolution system, of course, as is Call of Cthulhu, Runequest, Serenity, and most classic games. Hero Quest, Dust Devils, Dogs in the Vineyard, and Don't Rest Your Head are all conflict resolution systems.
Let's ignore for the moment the fact that many of the conflict resolution games are indie games, and that many of them do other things that are sometimes controversial.
So, what do you all think? If you haven't played both types, what's your gut impression? If you have, what's your experience?