The winners get to write history. At Shiloh, all the monuments were to Union units except for a DOC statue.
That is pretty much true. There is a large monument at Shiloh to Johnston, a new Tennessee monument, and a simple modern monument to Texans. There might be more Southern monuments, but that was what I saw on one afternoon visit.
Northern states came down and put up monument after monument. They dug up some of their soldiers who were buried in mass graves and reburied them in individual marked graves. The Southern economy was in shambles for years after the war, and consequently little got done as far as Southern monuments and reburying Southern soldiers. I visited one of the Southern mass graves only to find a Northern monument or two close to it and towering over it.
The same overabundance of Northern monuments compared to Southern ones is also true at Antietam/Sharpsburg.
The new Tennessee monument at Shiloh is moving.