I think you need to be more specific in order to get an answer here.

Which battle, which historians, and which first hand sources?

A vague answer to your vague question is that eyewitness reports of casualties are often incorrect. There is the confusion of battle, bad estimation, the need to over-report enemy dead to a fickle superior, the desire to downplay ones own losses... the r3asons for bad eyewitness accounts are many and vary depending on who is making the report. It is often up to a later historian to go through all of the various reports and figures to find a more accurate number.

In relation to the American Civil War, there is often disparities on each side. For example in the Battles of Fort Donelson and Fort Henry, each side reports different numbers. Grant would give a number and Floyd, Pillow, and Buckner would each give one as well. The numbers given are highly different. Grant underestimated the Confederates and the three confederate commanders underestimated the Union. This also extends to records of causality rates. The first years of the war aren't as recorded as the later years. In places like Andersonville (a Confederate ran POW camp), it was forbidden to write down the identity of the people who perished so the true number isn't known. There will always be a disparity in war especially when the war happened beforemodern technology. It should also be remembered that history is written by those who win.