Urban warfare is a tremendously difficult and dangerous task. Whether you are, as a political matter, "for" or "against" the US effort in Iraq, there is no doubt that the US forces have a done a tremendous job mastering the military science of urban warfare -- just compare, for example, the performance of the US in Fallujah with the performance of the Russian military in Grozny in January 1995, in which the forces that the Russians initially sent into Grozny were ambushed and largely wiped out. All indications are that the US military closely studied Russia's Grozny operations and drew valuable lessons from it.Particularly in this context, it is understandable that the newly-formed Iraqi Defense Forces (IDF) are not yet up to the standards of the US military -- no other army in the world is. I have not seen a definitive analysis of the performance of the IDF in Fallujah, but the buzz seems to be that they are getting better.
For these sorts of subjects, http://www.globalsecurity.org is an excellent resource.
Russian Disaster in Grozny 12/31/94 - 01/03/95: http://www.globalsecurity.org/military/library/report/2002/MOUTThomas.htm
Overview of Operation Dawn: http://www.globalsecurity.org/military/ops/oif-phantom-fury-fallujah.htm
US Assessment of IDF in Fallujah: http://www.globalsecurity.org/military/library/news/2004/11/mil-041119-afps01.htm