In this guide i will tell you about both sides of this civil war. And who you should support or join. Which you of course personally choose! You can also just be neutral or agaisnt both. Whatever you choose.

Sparta: The red side of the war. They are Militaristic and Authoritarian. Ruled by kings and a council. (Two kings in the game). They are also Traditionalists and Nationalists. Loyalty to Sparta above all. Also Oligarchic. Very Pragmatic and Ruthless. Expansion and survival is through strength.
The Sparta is also what storywise your family is. So if you want follow your family and how you was raised, Sparta is for you. And since Sparta is where and how you got raised, and your family is that. It means in the story there is ALOT Sparta stuff.
In idea of loot or stuff like this, Sparta gives alot cool unique stuff. But mostly, you get nothing that special.

Athens: The blue side of the war. They are Democratic. They are Progressive and Intellectual. They are also Imperialistic and Opportunistic. They build their Empire through naval dominance and tribute. Also they are Individualistic and Idealistic. Focused on freedom, creativity and personal glory.
At one point of story you will travel to Athens (Largest city in the game. Also modern day capital of Greece), its controlled by Athenians of course. And you will be working with local Athenians. Which also gives you alot info and experience how Athens think and work.
In idea of loot or stuff like this, Athens doesnt give that much of anything unique. So dont expect to get something cool or unique necessary by "siding" with Athens.

Historically, The Spartans won the war. So in case that helps you to choose side, awesome!
In the end, you cannot officially JOIN any of the sides. But you can choose dialogues that support one of the sides, and this effects of course in quests and main story and etc. You can also kind of roleplay, and target only one side of the war. Which i personally do. I personally side with Sparta always.
The game focuses more into that you are a mercenary. And you work for both sides, and do everything for money. But, many people including me, want to choose side in the war. So, that is why i made this guide.
NOTE: The game has regions, which most are controlled by either Athens or Sparta, and there is always conquest battles where you can choose side, if you win with the side you chose, the region is controlled now by the side you chose. BUT, when time flies, it will become weaker, and later there is again new battle. Also fighting with the side who DOES NOT control the region, gives you more rewards. Just so you know. And you CANNOT make the whole map fully Spartan, nor fully Athenian. Because first of all, there are certain regions that are always neutral. And certain regions that are ALWAYS Spartan or Athenian, AND IF you try make all the other regions only Spartan or Athenian, it wont really workout, because the more there is regions owned by one side, the more battles happen. And if you do not participate in the wars, the region owner will change. And if you have most map owned by one side, there will be alot battles sametime, and while you fight in one, after you finish that, one or more regions has changed sides. Because the battle got finished there. So do not try to change the whole map into only Spartan or only Athenian XD. Its pretty much impossible. And even if you manage to control it, you will NOT have time to do anything else but fight in conquest battles XD so not worth it.