Steven Den Beste discusses the three factions in the current war, which I have written about before, both directly and indirectly (see the list under the MORE... link). You should really read this, as it lays out the current conflict really well.
Note that there were originally four factions in this conflict. In addition to the West's internal conflict between what Den Beste calls the realists and the idealists, there was an internal conflict in the Arab/Muslim world between the islamists and the pan-Arab nationalists. These two sets of competing factions were pitted against each other by the attack of September 11. While pan-Arab nationalism was already in serious decline, I don't think that it's an exaggeration to say that the US destroyed that philosophy as a factor when we invaded and conquered Iraq. (Hopefully, we can have as devastating an effect on islamism by conquering Iran, which will be necessary within the next few years, I suspect.)
My posts on this topic include: