I suggested this game on Polsaker's Steam sale post without having actually played it. I did play Ultimate General Gettysburg, which I suppose was the sort of beta/demo to this game. It was pretty good but fairly short in comparison to Civil War, plus it had a cheap looking UI and some issues with unit balance/attributes.
Civil War is the best military RTS I've played outside of maybe Total War. It was actually made by a Total War modder, and some of the influence shows. The game does deal with the biggest problem that the Total War games had - the AI. AI in this game will fuck you up without remorse if you make even the slightest mistake. Flanking is difficult to pull off correctly and requires planning, you will find yourself outnumbered more often than not and the game has ditched the "sandbox" style of Total War and replaced it with a kind of sandbox-trigger event hybrid.
The American Civil War has never really interested me outside of it being an early example of "modern" fighting on display before WW1. It is not a requirement to have any interest in it to play this game, although I suspect you will probably do a lot better if you are familiar with certain battles. The entire campaign, or rather campaigns (there are two different ones for each side), are a retelling of the war. This is where the best part about this game comes in. Each battle is one individual mission, but they all flow into each other. Your units, their positions, casualties, experience etc. will carry on into the next phase of each battle, and then into the next battle.
If, for example, your best unit gets blown to pieces after you made an error, start the battle again. Sometimes it is actually better to lose a battle and save your troops than to win and have half of them slaughtered, because those troops might not be replaceable with the resources you have and you will need them in the next battle. This creates a sort of multilayered strategic approach to playing the game. You have your immediate goals of defending/attacking, your broader ones such as troop placement/condition in relation to how the later stages of the battle will pan out, but then you also need to think about the next battle and the one after that. All of these things need to be weighed before you make a decision.
The game doesn't have a full release yet so expect more content. Also, if you are going to play this game, consider starting on easy. I had a lot of trouble starting off even on easy, and I play a lot of these kinds of games.
I can second this recommendation. Ultimate General: Civil War is a great game.
I agree that in terms of troops control and management, it's among the best I've played. The campaign is actually a ton of fun, and I love how it's laid out, where you can optionally tackle some smaller battles before each "big battle" that advances the war forward. You gain (or lose) reputation as you fight battles, along with troops, equipment, and money. If you manage to do a fair bit of winning, you can either stock up your reputation for morale buffs in battle, or spend it to get certain bonuses (like a new commander, a famous unit, equipment, money, fresh bodies, and so on).
Managing equipment is actually meaningful. Most of your units will start with fairly basic weaponry, based on whether they are infantry, cavalry, or artillery units, but you can spend money to upgrade them to better stuff. One of the first things I did was upgrade my artillery to 12-pounder Napoleon guns, as they hit just the right combination of firepower, accuracy, and cost. I also upgraded a few of my infantry units to longer-ranged, more accurate muskets, and used that division as a specific long-ranged one. If you require too many men too quickly, it's possible to have a bottleneck on your equipment of choice for new units (but in my game I was playing the Rebs, so perhaps that played into it - the Union has more manpower and equipment, but the Confederacy has better morale and melee skill, as I recall).
And yeah, the game is hard. I also recommend easy.