The people at the Iraq Body Count project and the Oxford Research Group have released what appears to be a quite careful and judicious report counting and analyzing Iraqi civilian casualties since the beginning of the war. They count 24,865 civilians (just civilians, not soldiers or recruits or insurgents) killed in Iraq in the two years stretching from March 20, 2003 to March 19, 2005, and they estimate that there have been more than three injuries for every death. Nearly half of the reported deaths were in Baghdad (likely that proportion is so high in part because Baghdad is the best-reported of Iraq's conflict-ridden areas, and because of the good quality of mortuary data there); about one in every 500 Baghdad civilians has been killed violently since March 2003. Baghdad didn't have the highest number of civilian deaths per capita, though; that honor, among the larger cities, went to Fallujah, where the number rose to 1 in 136.
About 37% of those folks were killed by U.S. forces. Just under 11% were killed by insurgent forces, and about 5% were caught in cross-fire in which both groups participated. That leaves 36% killed in the continuing wave of violent crime that followed the war, enabled by the absence of police and the easy availability of weapons (this is an “excess” figure, subtracting out the average number of pre-war killings over a two-year period), and 11% who could not be classified.
The vast bulk of the 9,270 civilian killings by U.S.-led forces took place either in March 20-April 30 2003 (6882 reported civilian deaths, or 164 per day), or in April-November 2004 (2038 civilian deaths, or between eight and nine per day for the eight-month period). During other calendar periods, U.S.-led forces have killed, on average, fewer than one Iraqi civilian per day.
On the other hand, the number of civilian killings by insurgent forces, criminals, and unclassifiable actors (14,337 in all) has steadily increased over the two-year period, from a low of under 10 per day in April 2003 to a high of 35 per day in February 2005 (the last complete month in the study). As a result, the total number of civilians killed in the second year following the announced end of major hostilities was almost twice as high (11,315) as in the first (6,215).
(I should note that this was an actual count of actual deaths, not an estimate. It's limited to deaths that actually got reported to somebody whose records were good enough that they could be counted. For a more wide-ranging estimation, see Mortality before and after the 2003 invasion of Iraq: cluster sample study, published last fall in the Lancet, and concluding that “about 100 000 excess deaths, or more have happened since the 2003 invasion”).
I’m working from memory here but I believe the Lancet study also included non-violent deaths that could be considered “excess” in some meaningful way- deaths due to contaminated water and the like that were higher than before the war (since, say, purification plants were not working, either having been destroyed or else w/o electricity.) If the new study is only of violent deaths, and the lancet study included non-violent deaths, that would go a long way to explaining differences. (Please do correct me if I’m mistake about either study!)
Both of those are true, but that explains only a part of the difference; much more important, I think, is the fact that the Lancet figure is an estimate (which could be high) while the Iraq Body Count study is an actual count (which under difficult conditions will necessarily be low).