Very complex game, not as complex as Paradox's Victoria 2 but in this game its complex because it has so much you can do, unlike Vic 2 which is complex because the mechanics are not very well explained anywhere.
I like this game. I am British so I don't have any real feeling of immersion playing the American Civil War but like any strategy game its the act of fighting a strategic war, with historical troops, and finding out about things you didnt know about that makes this game really interesting.
The mechanics in this game are spot on. For example you dont move alone you move at the same time as the enemy does, so you have to predict where they are going to be and often you can get surprised. So thats very realistic. Far more realistic than attacking a paused enemy. Also you have very detailed heirarchy of troops including armies and corps, a lot like Paradox's Hearts of Iron 3 in fact. You get bonuses to things like supply and attack coordination for being well supported and organised which is good.
You can use gunboats to support your attacks, You can syncronise your attacks, You can even have neighbouring friendly armies 'march to the sound of guns' and automatically move to support you in a battle.
Pretty much everything you feel should be in the game is actually in the game, and yet this game is far more polished than the first game.
The only downsides are that the game might not be all that stable - many crashes have been reported and I had a critical error crash in the first tutorial, five minutes into the game on my first turn's generation, but none since. Also the GUI is rather bland looking compared to the lovely period one in the first game but its far easier to see whats going on and there are mods to add cosmetic improvements to it.
Overall I would say this is probably the best satrategic game I have ever played, I like it better than any of my Paradox games which are generally a bit simplistic in terms of game mechanics you have available to you. The Civil War is an interesting period of history as well in that both sides had it tough, the war was a long brutal one, with much movement and innovation. So its an interesting conflict to play.
So for playing an overall grand strategy wargame, where you can play through a whole war at strategic level whilst retaining the historical flavour of the period, and having some complexity where you always having a lot to think about both inside and outside the game, this probably is the best game you can play. It will certainly enourage you to find out more about the Civil War as well.
Whilst you are on I would also take a look at Ultimate General: Gettysberg, which is a fantastic tactical representation of the largest and most important Civil War battle, made by Darth Vader of Total War modding fame. It complements this game really well.