Erik has put a really quick and excellent synopsis of these very different games. In fact, it was pretty heroic being able to put all that together for games that are difficult to compare!
I agree with all he said. I will give the following caveats:
Forge of Freedom - A great game and probably the most detailed, realistic, and option packed simulation available (of ANY wargame out there) and certainly a great civil war sim. But even so, the economy is simpler than CoG stock, the game is still EXTREMELY complex. You can chose the upgrades of units, change the guns they carry, decide how much money to give to diplomacy, build one of several types of units and buildings in several dozen downs, interact with governors, fight gigantic (and extremely fun) hex-based turn-based battles, and deal with producing those four resources (you can even tweak production). So I would say that CoG:EE's simple economy is less complex than FoF, but I think that the options available in FoF are more compelling.
Advanced Tactics - Yes, Erik is right, AT is more of a "general" wargame with interesting mechanics and the ability to mod nearly anything. It isn't hard to play, which is why I love it, but it isn't the type of deep depth as War in the Pacific or Forge of Freedom. So the units seem a tad generic but the gameplay is not (and the units still have character). So AT is great for flexibility, and provides a neat Empire style game with a random map maker than is endless fun. The WWII setting is a bit of a veneer, but this isn't really the focus of such a great game.
Kharkov - I think Erik is perfectly right here, the game plays like one of those massive boardgames that simulate one major battle.
GWBTS - plays very little, other than the UI mechancis, like GG:AWD/WAW. An excellent game, a bit complex to grasp the command rules, but there is a lot to love here. I would say I prefer it's style to AACW.
"Neca eos omnes. Deus suos agnoscet!"
(Kill them all. God will know his own.)
-- Arnaud-Armaury, the Albigensian Crusade