I've often been struck by how resilient both these armies were throughout the war. Despite a number of conflicts, none were completely routed and devastated in one battle. Was this due to innefective cavalry, superior supply lines, changing technology, or something else?
In a previous post u/vonadler posted a great comment about how the US civil war armies would have stood up to European armies of the day.
This answer touches on the inability of American armies to force a decisive battle, and the various reasons for this failure, including their lack of cavalry and professional infantry that were willing or able to charge home when the other side waivered.
It might not be a complete answer for your question, but should provide a good starting point for you.
The book "Civil War Command and Strategy" by Archer Jones goes into great detail about why there were essentially no battles of annihilation in the Civil War.