Here's an excerpt showing that there was more mutal respect between the two sides than we sometimes see on message boards today.
Just back of these, and about equally distant from the creek, were the guards of the Confederate pickets. The sentinel on their post called out in like manner, "Turn out the guard for the commanding general," and, I believe, added, "General Grant." Their line in a moment front-faced to the north, facing me, and gave a salute, which I returned.
The most friendly relations seemed to exist between the pickets of the two armies. At one place there was a tree which had fallen across the stream, and which was used by the soldiers of both armies in drawing water for their camps. General Longstreet's corps was stationed there at the time, and wore blue of a little different shade from our uniform. Seeing a soldier in blue on this log, I rode up to him, commenced conversing with him, and asked whose corps he belonged to. He was very polite, and, touching his hat to me, said he belonged to General Longstreet's corps. I asked him a few questions--but not with a view of gaining any particular information--all of which he answered, and I rode off.